Pub Date : 2024-09-16DOI: 10.1088/1742-5468/ad6df3
Biao-Liang Ye, Qi-Cheng Wu, Bao-Qing Guo, Jun-Long Zhao, Yu-Liang Fang and Yan-Hui Zhou
In this paper, we investigate the cluster Ising model (CIM) via steered quantum coherence (SQC) and entropic uncertainty relation (EUR). We present the behavior of SQC quantified by the L1 norm, relative entropy and quantum Jensen–Shannon divergence. We also demonstrate the properties of EUR in the CIM. In addition, we provide a comparative analysis of these measures and present detailed numerical results.
{"title":"Steered quantum coherence and entropic uncertainty relation in the cluster Ising model","authors":"Biao-Liang Ye, Qi-Cheng Wu, Bao-Qing Guo, Jun-Long Zhao, Yu-Liang Fang and Yan-Hui Zhou","doi":"10.1088/1742-5468/ad6df3","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6df3","url":null,"abstract":"In this paper, we investigate the cluster Ising model (CIM) via steered quantum coherence (SQC) and entropic uncertainty relation (EUR). We present the behavior of SQC quantified by the L1 norm, relative entropy and quantum Jensen–Shannon divergence. We also demonstrate the properties of EUR in the CIM. In addition, we provide a comparative analysis of these measures and present detailed numerical results.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"42 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255299","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 : 2024-09-16DOI: 10.1088/1742-5468/ad6c31
Andrzej Chlebicki
We investigate the precision of the numerical implementation of the functional renormalization group based on extracting the eigenvalues from the linearized renormalization group transformation. For this purpose, we implement the local potential approximation and orders of the derivative expansion for the three-dimensional O(N) models with . We identify several categories of numerical error and devise simple tests to track their magnitude as functions of numerical parameters. Our numerical schemes converge properly and are characterized by errors of several orders of magnitude smaller than the error bars of the derivative expansion for these models. We highlight situations in which our methods cease to converge, most often due to rounding errors. In particular, we observe an impaired convergence of the discretization scheme when the grid is cut off at the value smaller than 3.5 times the local potential minimum. The program performing the numerical calculations for this study is shared as an open-source library accessible for review and reuse.
{"title":"Numerical accuracy of the derivative-expansion-based functional renormalization group","authors":"Andrzej Chlebicki","doi":"10.1088/1742-5468/ad6c31","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6c31","url":null,"abstract":"We investigate the precision of the numerical implementation of the functional renormalization group based on extracting the eigenvalues from the linearized renormalization group transformation. For this purpose, we implement the local potential approximation and orders of the derivative expansion for the three-dimensional O(N) models with . We identify several categories of numerical error and devise simple tests to track their magnitude as functions of numerical parameters. Our numerical schemes converge properly and are characterized by errors of several orders of magnitude smaller than the error bars of the derivative expansion for these models. We highlight situations in which our methods cease to converge, most often due to rounding errors. In particular, we observe an impaired convergence of the discretization scheme when the grid is cut off at the value smaller than 3.5 times the local potential minimum. The program performing the numerical calculations for this study is shared as an open-source library accessible for review and reuse.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"16 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255297","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 : 2024-09-16DOI: 10.1088/1742-5468/ad6976
Federico Corberi, Salvatore dello Russo and Luca Smaldone
We study the ordering kinetics of a generalization of the voter model with long-range interactions, the p-voter model, in one dimension. It is defined in terms of Boolean variables Si, agents or spins, located on sites i of a lattice, each of which takes in an elementary move the state of the majority of p other agents at distances r chosen with probability . For p = 2 the model can be exactly mapped onto the case with p = 1, which amounts to the voter model with long-range interactions decaying algebraically. For , instead, the dynamics falls into the universality class of the one-dimensional Ising model with long-ranged coupling constant quenched to small finite temperatures. In the limit , a crossover to the (different) behavior of the long-range Ising model quenched to zero temperature is observed. Since for p > 3 a closed set of differential equations cannot be found, we employed numerical simulations to address this case.
我们研究的是具有长程相互作用的选民模型的广义化，即一维的 p 选民模型的排序动力学。该模型由布尔变量 Si（代理或自旋）定义，代理或自旋位于晶格的 i 个位点上，每个代理在一次基本移动中，都会以概率为 . 的方式选择距离为 r 的 p 个其他代理的多数状态。当 p = 2 时，该模型可以完全映射到 p = 1 的情况，这相当于长程相互作用代数衰减的选民模型。而当 p = 2 时，动力学则属于一维伊辛模型的普遍性范畴，其长程耦合常数被淬火到很小的有限温度。在极限条件下，可以观察到与淬火到零温度的长程伊辛模型的（不同）行为交叉。由于无法找到 p > 3 的封闭微分方程组，我们采用了数值模拟来解决这种情况。
{"title":"Ordering kinetics with long-range interactions: interpolating between voter and Ising models","authors":"Federico Corberi, Salvatore dello Russo and Luca Smaldone","doi":"10.1088/1742-5468/ad6976","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6976","url":null,"abstract":"We study the ordering kinetics of a generalization of the voter model with long-range interactions, the p-voter model, in one dimension. It is defined in terms of Boolean variables Si, agents or spins, located on sites i of a lattice, each of which takes in an elementary move the state of the majority of p other agents at distances r chosen with probability . For p = 2 the model can be exactly mapped onto the case with p = 1, which amounts to the voter model with long-range interactions decaying algebraically. For , instead, the dynamics falls into the universality class of the one-dimensional Ising model with long-ranged coupling constant quenched to small finite temperatures. In the limit , a crossover to the (different) behavior of the long-range Ising model quenched to zero temperature is observed. Since for p > 3 a closed set of differential equations cannot be found, we employed numerical simulations to address this case.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"11 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255295","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 : 2024-09-16DOI: 10.1088/1742-5468/ad685b
Chandraniva Guha Ray, Indranil Mukherjee and P K Mohanty
We study a lattice gas (LG) model of hard-core particles on a square lattice experiencing nearest neighbour attraction J. Each particle has an internal orientation, independent of the others, that point towards one of the four nearest neighbour and it can move to the neighbouring site along that direction with the usual metropolis rate if the target site is vacant. The internal orientation of the particle can also change to any of the other three with a constant rate The dynamics of the model in reduces to that of the LG which exhibits a phase separation transition at particle density and temperature when the strength of attraction J crosses a threshold value This transition belongs to Ising universality class (IUC). For any finite the particles can be considered as attractive run-and-tumble particles (RTPs) in two dimensions with motility We find that RTPs also exhibit a phase separation transition, but the critical interaction required is which increases monotonically with increased motility It appears that the transition belongs to IUC. Surprisingly, in these models, motility impedes cluster formation process necessitating higher interaction to stabilize microscopic clusters. Moreover, MIPS like phases are not found when J = 0.
{"title":"How motility affects Ising transitions","authors":"Chandraniva Guha Ray, Indranil Mukherjee and P K Mohanty","doi":"10.1088/1742-5468/ad685b","DOIUrl":"https://doi.org/10.1088/1742-5468/ad685b","url":null,"abstract":"We study a lattice gas (LG) model of hard-core particles on a square lattice experiencing nearest neighbour attraction J. Each particle has an internal orientation, independent of the others, that point towards one of the four nearest neighbour and it can move to the neighbouring site along that direction with the usual metropolis rate if the target site is vacant. The internal orientation of the particle can also change to any of the other three with a constant rate The dynamics of the model in reduces to that of the LG which exhibits a phase separation transition at particle density and temperature when the strength of attraction J crosses a threshold value This transition belongs to Ising universality class (IUC). For any finite the particles can be considered as attractive run-and-tumble particles (RTPs) in two dimensions with motility We find that RTPs also exhibit a phase separation transition, but the critical interaction required is which increases monotonically with increased motility It appears that the transition belongs to IUC. Surprisingly, in these models, motility impedes cluster formation process necessitating higher interaction to stabilize microscopic clusters. Moreover, MIPS like phases are not found when J = 0.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"16 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255298","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 : 2024-09-16DOI: 10.1088/1742-5468/ad6efc
Yamen Hamdouni
We analytically derive the diffusion coefficients that drive a system of N coupled harmonic oscillators to an equilibrium state exhibiting persistent correlations. It is shown that the main effect of the latter consists in a renormalization of the natural frequencies and the friction coefficients of the oscillators. We find that the Einstein relation may be satisfied at low temperatures with frequency-dependent effective friction coefficients provided that the physical constraints are fulfilled. We also investigate entanglement evolution in a bipartite bosonic Bogoliubov system initially prepared in a thermal squeezed state. It is found that, in contrast to what one may expect, strong coupling slows down sudden death of the entanglement, and for initially separable states entanglement generation may occur.
我们通过分析推导出驱动 N 个耦合谐波振荡器系统达到平衡状态的扩散系数，该平衡状态表现出持久的相关性。结果表明，后者的主要影响在于振荡器固有频率和摩擦系数的重规范化。我们发现，在满足物理约束条件的前提下，爱因斯坦关系可以在低温下满足与频率相关的有效摩擦系数。我们还研究了最初在热挤压状态下制备的双玻色波哥留布夫系统中的纠缠演化。研究发现，与人们的预期相反，强耦合会减缓纠缠的猝死，而且对于最初可分离的状态，可能会产生纠缠。
{"title":"Diffusion coefficients preserving long-time correlations: consequences on the Einstein relation and on entanglement in a bosonic Bogoliubov system","authors":"Yamen Hamdouni","doi":"10.1088/1742-5468/ad6efc","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6efc","url":null,"abstract":"We analytically derive the diffusion coefficients that drive a system of N coupled harmonic oscillators to an equilibrium state exhibiting persistent correlations. It is shown that the main effect of the latter consists in a renormalization of the natural frequencies and the friction coefficients of the oscillators. We find that the Einstein relation may be satisfied at low temperatures with frequency-dependent effective friction coefficients provided that the physical constraints are fulfilled. We also investigate entanglement evolution in a bipartite bosonic Bogoliubov system initially prepared in a thermal squeezed state. It is found that, in contrast to what one may expect, strong coupling slows down sudden death of the entanglement, and for initially separable states entanglement generation may occur.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"213 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255300","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 : 2024-09-16DOI: 10.1088/1742-5468/ad65e5
Claude Godrèche and Jean-Marc Luck
Convex records have an appealing purely geometric definition. In a sequence of d-dimensional data points, the nth point is a convex record if it lies outside the convex hull of all preceding points. We specifically focus on the bivariate (i.e. two-dimensional) setting. For iid (independent and identically distributed) points, we establish an identity relating the mean number of convex records up to time n to the mean number of vertices in the convex hull of the first n points. By combining this identity with extensive numerical simulations, we provide a comprehensive overview of the statistics of convex records for various examples of iid data points in the plane: uniform points in the square and in the disk, Gaussian points and points with an isotropic power-law distribution. In all these cases, the mean values and variances of Nn and Rn grow proportionally to each other, resulting in the finite limit Fano factors FN and FR. We also consider planar random walks, i.e. sequences of points with iid increments. For both the Pearson walk in the continuum and the Pólya walk on a lattice, we characterise the growth of the mean number of convex records and demonstrate that the ratio keeps fluctuating with a universal limit distribution.
凸记录有一个吸引人的纯几何定义。在一个由 d 维数据点组成的序列中，如果第 n 个点位于前面所有点的凸壳之外，那么它就是一个凸记录。我们特别关注双变量（即二维）设置。对于 iid（独立且同分布）点，我们建立了一个特性，它将时间 n 前的凸记录平均数量与前 n 个点的凸壳中的顶点平均数量联系起来。通过将这一特性与大量的数值模拟相结合，我们全面概述了平面中不同实例的独立数据点的凸记录统计：方形和圆盘中的均匀点、高斯点和各向同性幂律分布的点。在所有这些情况下，Nn 和 Rn 的均值和方差都按比例增长，从而产生有限极限法诺因子 FN 和 FR。我们还考虑了平面随机漫步，即具有 iid 增量的点序列。对于连续体中的皮尔逊漫步和晶格上的波利亚漫步，我们都描述了凸记录平均数量的增长特征，并证明该比率以普遍的极限分布不断波动。
{"title":"On sequences of convex records in the plane","authors":"Claude Godrèche and Jean-Marc Luck","doi":"10.1088/1742-5468/ad65e5","DOIUrl":"https://doi.org/10.1088/1742-5468/ad65e5","url":null,"abstract":"Convex records have an appealing purely geometric definition. In a sequence of d-dimensional data points, the nth point is a convex record if it lies outside the convex hull of all preceding points. We specifically focus on the bivariate (i.e. two-dimensional) setting. For iid (independent and identically distributed) points, we establish an identity relating the mean number of convex records up to time n to the mean number of vertices in the convex hull of the first n points. By combining this identity with extensive numerical simulations, we provide a comprehensive overview of the statistics of convex records for various examples of iid data points in the plane: uniform points in the square and in the disk, Gaussian points and points with an isotropic power-law distribution. In all these cases, the mean values and variances of Nn and Rn grow proportionally to each other, resulting in the finite limit Fano factors FN and FR. We also consider planar random walks, i.e. sequences of points with iid increments. For both the Pearson walk in the continuum and the Pólya walk on a lattice, we characterise the growth of the mean number of convex records and demonstrate that the ratio keeps fluctuating with a universal limit distribution.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"195 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255263","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 : 2024-09-16DOI: 10.1088/1742-5468/ad6c2c
Sujit Kumar Nath and Sanjib Sabhapandit
We study the late-time exponential decay of the survival probability , of a one-dimensional run-and-tumble particle starting from with an initial orientation , under a confining potential with an absorbing boundary at . We find that the decay rate of the survival probability has a strong dependence on the location a of the absorbing boundary, which undergoes a freezing transition at a critical value , where is the self-propulsion speed and γ is the tumbling rate of the particle. For , the value of increases monotonically from zero, as a decreases from infinity, until it attains the maximum value at . For , the value of freezes to the value . We also obtain the propagator with the absorbing boundary condition at x = a. Our analytical results are supported by numerical simulations.
我们研究了一维翻滚粒子的存活概率Ⅴ的晚期指数衰减，该粒子从初始方向Ⅴ开始，在约束势下的存活概率Ⅴ在Ⅴ处有一个吸收边界。我们发现存活概率的衰减率与吸收边界的位置 a 有很大关系，吸收边界在临界值 , 时发生冻结转变，其中 , 是自推进速度，γ 是粒子的翻滚速率。对于 ，γ 的值冻结在 。我们还得到了在 x = a 处具有吸收边界条件的传播者。我们的分析结果得到了数值模拟的支持。
{"title":"Survival probability and position distribution of a run and tumble particle in U ( x ) ...","authors":"Sujit Kumar Nath and Sanjib Sabhapandit","doi":"10.1088/1742-5468/ad6c2c","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6c2c","url":null,"abstract":"We study the late-time exponential decay of the survival probability , of a one-dimensional run-and-tumble particle starting from with an initial orientation , under a confining potential with an absorbing boundary at . We find that the decay rate of the survival probability has a strong dependence on the location a of the absorbing boundary, which undergoes a freezing transition at a critical value , where is the self-propulsion speed and γ is the tumbling rate of the particle. For , the value of increases monotonically from zero, as a decreases from infinity, until it attains the maximum value at . For , the value of freezes to the value . We also obtain the propagator with the absorbing boundary condition at x = a. Our analytical results are supported by numerical simulations.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"16 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255296","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 : 2024-09-09DOI: 10.1088/1742-5468/ad72db
Tânia Tomé, Mário J de Oliveira
We propose an expression for the production of entropy for a system described by a stochastic dynamics which is appropriate for the case where the reverse transition rate vanishes but the forward transition is nonzero. The expression is positive definite and based on the inequality xlnx−(x−1)⩾0. The corresponding entropy flux is linear in the probability distribution allowing its calculation as an average. The expression is applied to the one-dimensional contact process at the stationary state. We found that the rate of entropy production per site is finite with a singularity at the critical point with diverging slope.
{"title":"Entropy production of the contact model","authors":"Tânia Tomé, Mário J de Oliveira","doi":"10.1088/1742-5468/ad72db","DOIUrl":"https://doi.org/10.1088/1742-5468/ad72db","url":null,"abstract":"We propose an expression for the production of entropy for a system described by a stochastic dynamics which is appropriate for the case where the reverse transition rate vanishes but the forward transition is nonzero. The expression is positive definite and based on the inequality <inline-formula>\u0000<tex-math><?CDATA $xln x-(x-1)unicode{x2A7E}0$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>x</mml:mi><mml:mi>ln</mml:mi><mml:mo></mml:mo><mml:mi>x</mml:mi><mml:mo>−</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>x</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo><mml:mtext>⩾</mml:mtext><mml:mn>0</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad72dbieqn1.gif\"></inline-graphic></inline-formula>. The corresponding entropy flux is linear in the probability distribution allowing its calculation as an average. The expression is applied to the one-dimensional contact process at the stationary state. We found that the rate of entropy production per site is finite with a singularity at the critical point with diverging slope.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"11 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188497","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 : 2024-09-09DOI: 10.1088/1742-5468/ad72d9
Abha Singh, Rahul Chhimpa, Avinash Chand Yadav
We consider the Robin Hood dynamics, a one-dimensional extremal self-organized critical model that describes the low-temperature creep phenomenon. One of the key quantities is the time evolution of the state variable (force noise). To understand the temporal correlations, we compute the power spectra of the local force fluctuations and apply finite-size scaling to get scaling functions and critical exponents. We find a signature of the 1/fα noise for the local force with a nontrivial value of the spectral exponent 0<α<2. We also examine temporal fluctuations in the position of the extremal site and a local activity signal. We present results for different local interaction rules of the model.
{"title":"1/fα noise in the Robin Hood model","authors":"Abha Singh, Rahul Chhimpa, Avinash Chand Yadav","doi":"10.1088/1742-5468/ad72d9","DOIUrl":"https://doi.org/10.1088/1742-5468/ad72d9","url":null,"abstract":"We consider the Robin Hood dynamics, a one-dimensional extremal self-organized critical model that describes the low-temperature creep phenomenon. One of the key quantities is the time evolution of the state variable (force noise). To understand the temporal correlations, we compute the power spectra of the local force fluctuations and apply finite-size scaling to get scaling functions and critical exponents. We find a signature of the <inline-formula>\u0000<tex-math><?CDATA $1/f^{alpha}$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:msup><mml:mi>f</mml:mi><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad72d9ieqn3.gif\"></inline-graphic></inline-formula> noise for the local force with a nontrivial value of the spectral exponent <inline-formula>\u0000<tex-math><?CDATA $0 lt alpha lt 2$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mn>0</mml:mn><mml:mo><</mml:mo><mml:mi>α</mml:mi><mml:mo><</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad72d9ieqn4.gif\"></inline-graphic></inline-formula>. We also examine temporal fluctuations in the position of the extremal site and a local activity signal. We present results for different local interaction rules of the model.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"13 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188495","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 : 2024-09-09DOI: 10.1088/1742-5468/ad72da
Fangfang Wang, Wei Liu, Jun Ma, Kai Qi, Ying Tang, Zengru Di
This research provides a examination of transitions within the various-state Potts model in two-dimensional finite-size lattices. Leveraging the Wang–Landau sampling and parallel tempering, we systematically obtain the density of states, facilitating a comprehensive comparative analysis of the results. The determination of the third-order transitions location are achieved through a meticulous examination of the density of states using microcanonical inflection-point analysis. The remarkable alignment between canonical and microcanonical results for higher-order transition locations affirms the universality of these transitions. Our results further illustrate the universality of the robust and microcanonical inflection-point analysis of Wang–Landau sampling.
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