Pub Date : 2024-05-22DOI: 10.1088/1742-5468/ad41db
Federico Corberi and Luca Smaldone
We investigate the aging properties of the one-dimensional voter model with long-range interactions in its ordering kinetics. In this system, an agent, , positioned at a lattice vertex i, copies the state of another one located at a distance r, selected randomly with a probability . Employing both analytical and numerical methods, we compute the two-time correlation function ( ) between the state of a variable Si at time s and that of another one, at distance r, at time t. At time t, the memory of an agent of its former state at time s, expressed by the autocorrelation function , decays algebraically for α > 1 as , where L is a time-increasing coherence length and λ is the Fisher–Huse exponent. We find λ = 1 for α > 2, and for . For , instead, there is an exponential decay, as in the mean field. Then, in contrast with what is known for the related Ising model, here we find that λ increases upon decreasing α. The space-dependent correlation obeys a scaling symmetry for α > 2. Similarly, for , one has , where the length regulating two-time correlations now differs from the coherence length as , with .
我们研究了在排序动力学中具有长程相互作用的一维投票者模型的老化特性。在这个系统中，一个位于网格顶点 i 的代理复制了另一个位于距离 r 处的代理的状态，这个代理是以概率......随机选择的。利用分析和数值方法，我们计算了一个变量 Si 在 s 时刻的状态与另一个变量 r 在 t 时刻的状态之间的双时相关函数（ ）。在 t 时刻，一个代理对其在 s 时刻的前状态的记忆，用自相关函数 表示，在 α > 1 时代数衰减为 ，其中 L 是时间递增的相干长度，λ 是费雪-胡斯指数。我们发现，当 α > 2 时，λ = 1；当 α > 2 时，λ = 1。而对于 ，则会出现指数衰减，就像在平均场中一样。那么，与相关伊辛模型的已知情况相反，在这里我们发现 λ 会随着 α 的减小而增大。同样，对于Ⅳ，我们可以得到Ⅴ，此时调节两时相关性的长度与相干长度的差别为Ⅴ。
{"title":"Aging properties of the voter model with long-range interactions","authors":"Federico Corberi and Luca Smaldone","doi":"10.1088/1742-5468/ad41db","DOIUrl":"https://doi.org/10.1088/1742-5468/ad41db","url":null,"abstract":"We investigate the aging properties of the one-dimensional voter model with long-range interactions in its ordering kinetics. In this system, an agent, , positioned at a lattice vertex i, copies the state of another one located at a distance r, selected randomly with a probability . Employing both analytical and numerical methods, we compute the two-time correlation function ( ) between the state of a variable Si at time s and that of another one, at distance r, at time t. At time t, the memory of an agent of its former state at time s, expressed by the autocorrelation function , decays algebraically for α > 1 as , where L is a time-increasing coherence length and λ is the Fisher–Huse exponent. We find λ = 1 for α > 2, and for . For , instead, there is an exponential decay, as in the mean field. Then, in contrast with what is known for the related Ising model, here we find that λ increases upon decreasing α. The space-dependent correlation obeys a scaling symmetry for α > 2. Similarly, for , one has , where the length regulating two-time correlations now differs from the coherence length as , with .","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"33 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141148241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-22DOI: 10.1088/1742-5468/ad4538
Sourav Manna, Błażej Jaworowski and Anne E B Nielsen
We study many-body localization in a hardcore boson model in the presence of random disorder on finite generation fractal lattices with different Hausdorff dimensions and different local lattice structures. In particular, we consider the Vicsek, T-shaped, Sierpinski gasket, and modified Koch-curve fractal lattices. In the single-particle case, these systems display Anderson localization for arbitrary disorder strength if they are large enough. In the many-body case, the systems available to exact diagonalization exhibit a transition between a delocalized and localized regime, visible in the spectral and entanglement properties of these systems. The position of this transition depends on the Hausdorff dimension of the given fractal, as well as on its local structure.
{"title":"Many-body localization on finite generation fractal lattices","authors":"Sourav Manna, Błażej Jaworowski and Anne E B Nielsen","doi":"10.1088/1742-5468/ad4538","DOIUrl":"https://doi.org/10.1088/1742-5468/ad4538","url":null,"abstract":"We study many-body localization in a hardcore boson model in the presence of random disorder on finite generation fractal lattices with different Hausdorff dimensions and different local lattice structures. In particular, we consider the Vicsek, T-shaped, Sierpinski gasket, and modified Koch-curve fractal lattices. In the single-particle case, these systems display Anderson localization for arbitrary disorder strength if they are large enough. In the many-body case, the systems available to exact diagonalization exhibit a transition between a delocalized and localized regime, visible in the spectral and entanglement properties of these systems. The position of this transition depends on the Hausdorff dimension of the given fractal, as well as on its local structure.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"1 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141148292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-19DOI: 10.1088/1742-5468/ad401e
Lorenzo Correale and Alessandro Silva
We study the non-equilibrium phase diagram of a fully-connected Ising p-spin model, for generic p > 2, and investigate its robustness with respect to the inclusion of spin-wave fluctuations, resulting from a ferromagnetic, short-range spin interaction. In particular, we investigate the dynamics of the mean-field model after a quantum quench: we observe a new dynamical phase transition which is either first or second order depending on the even or odd parity of p, in stark contrast with its thermal counterpart which is first order for all p. The dynamical phase diagram is qualitatively modified by the fluctuations introduced by a short-range interaction which drive the system always towards various prethermal paramagnetic phases determined by the strength of time dependent fluctuations of the magnetization.
我们研究了一般 p > 2 的全连接伊辛 p-自旋模型的非平衡相图，并研究了它在包含铁磁短程自旋相互作用产生的自旋波波动时的稳健性。我们特别研究了量子淬火后均势场模型的动力学：我们观察到一个新的动力学相变，它是一阶或二阶的，取决于 p 的偶数或奇数奇偶性，这与热对应相变形成鲜明对比，后者对所有 p 都是一阶的。
{"title":"Changing the order of a dynamical phase transition through fluctuations in a quantum p-spin model","authors":"Lorenzo Correale and Alessandro Silva","doi":"10.1088/1742-5468/ad401e","DOIUrl":"https://doi.org/10.1088/1742-5468/ad401e","url":null,"abstract":"We study the non-equilibrium phase diagram of a fully-connected Ising p-spin model, for generic p > 2, and investigate its robustness with respect to the inclusion of spin-wave fluctuations, resulting from a ferromagnetic, short-range spin interaction. In particular, we investigate the dynamics of the mean-field model after a quantum quench: we observe a new dynamical phase transition which is either first or second order depending on the even or odd parity of p, in stark contrast with its thermal counterpart which is first order for all p. The dynamical phase diagram is qualitatively modified by the fluctuations introduced by a short-range interaction which drive the system always towards various prethermal paramagnetic phases determined by the strength of time dependent fluctuations of the magnetization.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"18 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141148244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-15DOI: 10.1088/1742-5468/ad37be
Gernot Akemann, Nayden Chakarov, Oliver Krüger, Adam Mielke, Meinolf Ottensmann and Patricia Pässler
The two-dimensional (2D) Coulomb gas is a one-parameter family of random point processes, depending on the inverse temperature β. Based on previous work, it is proposed as a simple statistical measure to quantify the intra- and interspecies repulsion among three different highly territorial birds of prey. Using data from the area of the Teutoburger Wald over 20 years, we fit the nearest-neighbour and next-to-nearest neighbour spacing distributions between the respective nests of the goshawk, eagle owl and the previously examined common buzzard to β of the Coulomb gas. Within each species, the repulsion measured in this way deviates significantly from the Poisson process of independent points in the plane. In contrast, the repulsion amongst each of two species is found to be considerably lower and closer to Poisson. Methodologically, we investigate the influence of the terrain, of a shorter interaction range given by the 2D Yukawa interaction, and the statistical independence of the time moving average we use for the yearly ensembles of occupied nests. We also check that an artificial random displacement of the original nest positions of the order of the mean level spacing quickly destroys the repulsion measured by β > 0. A simple, approximate analytical expression for the nearest-neighbour spacing distribution derived from non-Hermitian random matrix theory proves to be very useful.
{"title":"Interactions between different birds of prey as a random point process","authors":"Gernot Akemann, Nayden Chakarov, Oliver Krüger, Adam Mielke, Meinolf Ottensmann and Patricia Pässler","doi":"10.1088/1742-5468/ad37be","DOIUrl":"https://doi.org/10.1088/1742-5468/ad37be","url":null,"abstract":"The two-dimensional (2D) Coulomb gas is a one-parameter family of random point processes, depending on the inverse temperature β. Based on previous work, it is proposed as a simple statistical measure to quantify the intra- and interspecies repulsion among three different highly territorial birds of prey. Using data from the area of the Teutoburger Wald over 20 years, we fit the nearest-neighbour and next-to-nearest neighbour spacing distributions between the respective nests of the goshawk, eagle owl and the previously examined common buzzard to β of the Coulomb gas. Within each species, the repulsion measured in this way deviates significantly from the Poisson process of independent points in the plane. In contrast, the repulsion amongst each of two species is found to be considerably lower and closer to Poisson. Methodologically, we investigate the influence of the terrain, of a shorter interaction range given by the 2D Yukawa interaction, and the statistical independence of the time moving average we use for the yearly ensembles of occupied nests. We also check that an artificial random displacement of the original nest positions of the order of the mean level spacing quickly destroys the repulsion measured by β > 0. A simple, approximate analytical expression for the nearest-neighbour spacing distribution derived from non-Hermitian random matrix theory proves to be very useful.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"206 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-01DOI: 10.1088/1742-5468/ad3a5d
Jozef Sznajd
Three 2D spin models made of frustrated zig-zag chains with competing interactions which, by exact summation with respect to some degrees of freedom, can be replaced by an effective temperature-dependent interaction, were considered. The first model, exactly solvable Ising chains coupled by only four-spin interactions, does not exhibit any finite temperature phase transition; nevertheless, temperature can trigger a frustration–no frustration crossover accompanied by gigantic specific heat. A similar effect was observed in several two-leg ladder models (Weiguo 2020 arXiv:2006.08921v2; 2020 2006.15087v1). The anisotropic Ising chains coupled by a direct interchain interaction and, competing with it, indirect interaction via spins located between chains, are analyzed using the exact Onsager’s equation and linear perturbation renormalization group (LPRG). Depending on the parameter set, such a model exhibits one antiferromagnetic (AF) or ferromagnetic (FM) phase transition or three phase transitions with a re-entrant disordered phase between AF and FM ones. The LPRG method was also used to study coupled uniaxial XXZ chains which, for example, can be a minimal model to describe the magnetic properties of compounds in which uranium and rare earth atoms form zig-zag chains. As with the Ising model, for a certain set of parameters, the model can undergo three phase transitions. However, both intrachain and interchain plain interactions si,jxsk,lx+si,jysk,ly can eliminate the re-entrant disordered phase, and then only one transition takes place. Additionally, the XXZ model can undergo temperature-induced metamagnetic transition.
研究考虑了三种二维自旋模型，它们由具有竞争相互作用的沮陷之字链组成，通过对某些自由度的精确求和，这些相互作用可以被有效的温度相关相互作用所取代。第一个模型是仅由四自旋相互作用耦合的精确可解伊辛链，它没有表现出任何有限温度相变；然而，温度会引发沮度-非沮度交叉，并伴随着巨大的比热。在一些两腿梯形模型中也观察到了类似的效应（魏国，2020 arXiv:2006.08921v2；2020 2006.15087v1）。利用精确的昂萨格方程和线性扰动重正化群（LPRG）分析了各向异性伊辛链与链间的直接相互作用以及链间自旋的间接相互作用。根据参数设置的不同，这种模型表现出一种反铁磁性（AF）或铁磁性（FM）相变，或三种相变，其中在 AF 和 FM 相变之间有一个重入无序相。LPRG 方法还用于研究耦合单轴 XXZ 链，例如，它可以作为描述铀和稀土原子形成之字链的化合物磁性能的最小模型。与伊辛模型一样，在一定的参数设置下，该模型可以发生三种相变。然而，链内和链间的平素相互作用 si,jxsk,lx+si,jysk,ly 可以消除再入无序相，这时只发生一种转变。此外，XXZ 模型还可能发生温度诱导的元磁转变。
{"title":"Frustration—no frustration crossover and phase transitions in 2D spin models with zig-zag structures","authors":"Jozef Sznajd","doi":"10.1088/1742-5468/ad3a5d","DOIUrl":"https://doi.org/10.1088/1742-5468/ad3a5d","url":null,"abstract":"Three 2D spin models made of frustrated zig-zag chains with competing interactions which, by exact summation with respect to some degrees of freedom, can be replaced by an effective temperature-dependent interaction, were considered. The first model, exactly solvable Ising chains coupled by only four-spin interactions, does not exhibit any finite temperature phase transition; nevertheless, temperature can trigger a frustration–no frustration crossover accompanied by gigantic specific heat. A similar effect was observed in several two-leg ladder models (Weiguo 2020 arXiv:<ext-link ext-link-type=\"arxiv\" xlink:href=\"https://arxiv.org/abs/2006.08921v2\" xlink:type=\"simple\">2006.08921v2</ext-link>; 2020 <ext-link ext-link-type=\"uri\" xlink:href=\"https://arxiv.org/abs/2006.15087v1\" xlink:type=\"simple\">2006.15087v1</ext-link>). The anisotropic Ising chains coupled by a direct interchain interaction and, competing with it, indirect interaction via spins located between chains, are analyzed using the exact Onsager’s equation and linear perturbation renormalization group (LPRG). Depending on the parameter set, such a model exhibits one antiferromagnetic (AF) or ferromagnetic (FM) phase transition or three phase transitions with a re-entrant disordered phase between AF and FM ones. The LPRG method was also used to study coupled uniaxial <italic toggle=\"yes\">XXZ</italic> chains which, for example, can be a minimal model to describe the magnetic properties of compounds in which uranium and rare earth atoms form zig-zag chains. As with the Ising model, for a certain set of parameters, the model can undergo three phase transitions. However, both intrachain and interchain plain interactions <inline-formula>\u0000<tex-math><?CDATA $s_{i,j}^x s_{k,l}^x+s_{i,j}^y s_{k,l}^y$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:msubsup><mml:mi>s</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msubsup><mml:msubsup><mml:mi>s</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>l</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>s</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow><mml:mi>y</mml:mi></mml:msubsup><mml:msubsup><mml:mi>s</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>l</mml:mi></mml:mrow><mml:mi>y</mml:mi></mml:msubsup></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad3a5dieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> can eliminate the re-entrant disordered phase, and then only one transition takes place. Additionally, the <italic toggle=\"yes\">XXZ</italic> model can undergo temperature-induced metamagnetic transition.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"18 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140835358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-30DOI: 10.1088/1742-5468/ad3a5e
Eric Bertin, Alexandre Solon
We propose a one-dimensional model of active particles interpolating between quorum sensing models used in the study of motility-induced phase separation (MIPS) and models of congestion of traffic flow on a single-lane highway. Particles have a target velocity with a density-dependent magnitude and a direction that flips with a finite rate that is biased toward moving right. Two key parameters are the bias and the speed relaxation time. MIPS is known to occur in such models at zero bias and zero relaxation time (overdamped dynamics), while a fully biased motion with no velocity reversal models traffic flow on a highway. Using both numerical simulations and continuum equations derived from the microscopic dynamics, we show that a single phase-separated state extends from the usual MIPS to congested traffic flow in the phase diagram defined by the bias and the speed relaxation time. However, in the fully biased case, inertia is essential to observe phase separation, making MIPS and congested traffic flow seemingly different phenomena if not simultaneously considering inertia and tumbling. We characterize the velocity of the dense phase, which is static for usual MIPS and moves backward in traffic congestion. We also find that in presence of bias, the phase diagram becomes richer, with an additional transition between phase separation and a microphase separation that is seen above a threshold bias or relaxation rate.
{"title":"Biased motility-induced phase separation: from chemotaxis to traffic jams","authors":"Eric Bertin, Alexandre Solon","doi":"10.1088/1742-5468/ad3a5e","DOIUrl":"https://doi.org/10.1088/1742-5468/ad3a5e","url":null,"abstract":"We propose a one-dimensional model of active particles interpolating between quorum sensing models used in the study of motility-induced phase separation (MIPS) and models of congestion of traffic flow on a single-lane highway. Particles have a target velocity with a density-dependent magnitude and a direction that flips with a finite rate that is biased toward moving right. Two key parameters are the bias and the speed relaxation time. MIPS is known to occur in such models at zero bias and zero relaxation time (overdamped dynamics), while a fully biased motion with no velocity reversal models traffic flow on a highway. Using both numerical simulations and continuum equations derived from the microscopic dynamics, we show that a single phase-separated state extends from the usual MIPS to congested traffic flow in the phase diagram defined by the bias and the speed relaxation time. However, in the fully biased case, inertia is essential to observe phase separation, making MIPS and congested traffic flow seemingly different phenomena if not simultaneously considering inertia and tumbling. We characterize the velocity of the dense phase, which is static for usual MIPS and moves backward in traffic congestion. We also find that in presence of bias, the phase diagram becomes richer, with an additional transition between phase separation and a microphase separation that is seen above a threshold bias or relaxation rate.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"30 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140835365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-23DOI: 10.1088/1742-5468/ad3199
Bart Wijns, Ralf Eichhorn and Bart Cleuren
A microscopic model for a translational Brownian motor, dubbed a Brownian translator, is introduced. It is inspired by the Brownian gyrator described by Filliger and Reimann (2007 Phys. Rev. Lett.99 230602). The Brownian translator consists of a spatially asymmetric object moving freely along a line due to perpetual collisions with a surrounding ideal gas. When this gas has an anisotropic temperature, both spatial and temporal symmetries are broken and the object acquires a nonzero drift. Onsager reciprocity implies the opposite phenomenon, that is dragging a spatially asymmetric object into an (initially at) equilibrium gas induces an energy flow that results in anisotropic gas temperatures. Expressions for the dynamical and energetic properties are derived as a series expansion in the mass ratio (of gas particle vs. object). These results are in excellent agreement with molecular dynamics simulations.
{"title":"Microscopic model for a Brownian translator","authors":"Bart Wijns, Ralf Eichhorn and Bart Cleuren","doi":"10.1088/1742-5468/ad3199","DOIUrl":"https://doi.org/10.1088/1742-5468/ad3199","url":null,"abstract":"A microscopic model for a translational Brownian motor, dubbed a Brownian translator, is introduced. It is inspired by the Brownian gyrator described by Filliger and Reimann (2007 Phys. Rev. Lett.99 230602). The Brownian translator consists of a spatially asymmetric object moving freely along a line due to perpetual collisions with a surrounding ideal gas. When this gas has an anisotropic temperature, both spatial and temporal symmetries are broken and the object acquires a nonzero drift. Onsager reciprocity implies the opposite phenomenon, that is dragging a spatially asymmetric object into an (initially at) equilibrium gas induces an energy flow that results in anisotropic gas temperatures. Expressions for the dynamical and energetic properties are derived as a series expansion in the mass ratio (of gas particle vs. object). These results are in excellent agreement with molecular dynamics simulations.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"9 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140801586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-23DOI: 10.1088/1742-5468/ad3ccf
Kevin Bauerbach and Florian Gebhard
We determine the impurity-induced free energy and the impurity-induced zero-field susceptibility of the symmetric single-impurity Kondo model from weak-coupling perturbation theory up to third order in the Kondo coupling at low temperatures and small magnetic fields. We reproduce the analytical structure of the zero-field magnetic susceptibility as obtained from Wilson’s renormalization group method. This permits us to obtain analytically the first two Wilson numbers.
{"title":"Second Wilson number from third-order perturbation theory for the symmetric single-impurity Kondo model at low temperatures","authors":"Kevin Bauerbach and Florian Gebhard","doi":"10.1088/1742-5468/ad3ccf","DOIUrl":"https://doi.org/10.1088/1742-5468/ad3ccf","url":null,"abstract":"We determine the impurity-induced free energy and the impurity-induced zero-field susceptibility of the symmetric single-impurity Kondo model from weak-coupling perturbation theory up to third order in the Kondo coupling at low temperatures and small magnetic fields. We reproduce the analytical structure of the zero-field magnetic susceptibility as obtained from Wilson’s renormalization group method. This permits us to obtain analytically the first two Wilson numbers.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"1 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140801301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-23DOI: 10.1088/1742-5468/ad3a5c
Ken Yamamoto, Takashi Bando, Hirokazu Yanagawa and Yoshihiro Yamazaki
The double Pareto distribution is a heavy-tailed distribution with a power-law tail, that is generated via geometric Brownian motion with an exponentially distributed observation time. In this study, we examine a modified model wherein the exponential distribution of the observation time is replaced with a continuous uniform distribution. The probability density, complementary cumulative distribution, and moments of this model are exactly calculated. Furthermore, the validity of the analytical calculations is discussed in comparison with numerical simulations of stochastic processes.
{"title":"Deformation of power law in the double Pareto distribution using uniformly distributed observation time","authors":"Ken Yamamoto, Takashi Bando, Hirokazu Yanagawa and Yoshihiro Yamazaki","doi":"10.1088/1742-5468/ad3a5c","DOIUrl":"https://doi.org/10.1088/1742-5468/ad3a5c","url":null,"abstract":"The double Pareto distribution is a heavy-tailed distribution with a power-law tail, that is generated via geometric Brownian motion with an exponentially distributed observation time. In this study, we examine a modified model wherein the exponential distribution of the observation time is replaced with a continuous uniform distribution. The probability density, complementary cumulative distribution, and moments of this model are exactly calculated. Furthermore, the validity of the analytical calculations is discussed in comparison with numerical simulations of stochastic processes.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"10 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140801385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-22DOI: 10.1088/1742-5468/ad343b
Nicolò Ruggeri, Alessandro Lonardi and Caterina De Bacco
Hypergraphs are widely adopted tools to examine systems with higher-order interactions. Despite recent advancements in methods for community detection in these systems, we still lack a theoretical analysis of their detectability limits. Here, we derive closed-form bounds for community detection in hypergraphs. Using a message-passing formulation, we demonstrate that detectability depends on the hypergraphs’ structural properties, such as the distribution of hyperedge sizes or their assortativity. Our formulation enables a characterization of the entropy of a hypergraph in relation to that of its clique expansion, showing that community detection is enhanced when hyperedges highly overlap on pairs of nodes. We develop an efficient message-passing algorithm to learn communities and model parameters on large systems. Additionally, we devise an exact sampling routine to generate synthetic data from our probabilistic model. Using these methods, we numerically investigate the boundaries of community detection in synthetic datasets, and extract communities from real systems. Our results extend our understanding of the limits of community detection in hypergraphs and introduce flexible mathematical tools to study systems with higher-order interactions.
{"title":"Message-passing on hypergraphs: detectability, phase transitions and higher-order information","authors":"Nicolò Ruggeri, Alessandro Lonardi and Caterina De Bacco","doi":"10.1088/1742-5468/ad343b","DOIUrl":"https://doi.org/10.1088/1742-5468/ad343b","url":null,"abstract":"Hypergraphs are widely adopted tools to examine systems with higher-order interactions. Despite recent advancements in methods for community detection in these systems, we still lack a theoretical analysis of their detectability limits. Here, we derive closed-form bounds for community detection in hypergraphs. Using a message-passing formulation, we demonstrate that detectability depends on the hypergraphs’ structural properties, such as the distribution of hyperedge sizes or their assortativity. Our formulation enables a characterization of the entropy of a hypergraph in relation to that of its clique expansion, showing that community detection is enhanced when hyperedges highly overlap on pairs of nodes. We develop an efficient message-passing algorithm to learn communities and model parameters on large systems. Additionally, we devise an exact sampling routine to generate synthetic data from our probabilistic model. Using these methods, we numerically investigate the boundaries of community detection in synthetic datasets, and extract communities from real systems. Our results extend our understanding of the limits of community detection in hypergraphs and introduce flexible mathematical tools to study systems with higher-order interactions.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"28 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140801303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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