William Y. Wang, Stephen J. Thornton, Bulbul Chakraborty, Anna Barth, Navneet Singh, Japheth Omonira, Jonathan A. Michel, Moumita Das, James P. Sethna, Itai Cohen
We study how the rigidity transition in a triangular lattice changes as a function of anisotropy by preferentially filling bonds on the lattice in one direction. We discover that the onset of rigidity in anisotropic spring networks arises in at least two steps, reminiscent of the two-step melting transition in two dimensional crystals. In particular, our simulations demonstrate that the percolation of stress-supporting bonds happens at different critical volume fractions along different directions. By examining each independent component of the elasticity tensor, we determine universal exponents and develop universal scaling functions to analyze isotropic rigidity percolation as a multicritical point. We expect that these results will be important for elucidating the underlying mechanical phase transitions governing the properties of biological materials ranging from the cytoskeletons of cells to the extracellular networks of tissues such as tendon where the networks are often preferentially aligned.
{"title":"Rigidity transitions in anisotropic networks happen in multiple steps","authors":"William Y. Wang, Stephen J. Thornton, Bulbul Chakraborty, Anna Barth, Navneet Singh, Japheth Omonira, Jonathan A. Michel, Moumita Das, James P. Sethna, Itai Cohen","doi":"arxiv-2409.08565","DOIUrl":"https://doi.org/arxiv-2409.08565","url":null,"abstract":"We study how the rigidity transition in a triangular lattice changes as a\u0000function of anisotropy by preferentially filling bonds on the lattice in one\u0000direction. We discover that the onset of rigidity in anisotropic spring\u0000networks arises in at least two steps, reminiscent of the two-step melting\u0000transition in two dimensional crystals. In particular, our simulations\u0000demonstrate that the percolation of stress-supporting bonds happens at\u0000different critical volume fractions along different directions. By examining\u0000each independent component of the elasticity tensor, we determine universal\u0000exponents and develop universal scaling functions to analyze isotropic rigidity\u0000percolation as a multicritical point. We expect that these results will be\u0000important for elucidating the underlying mechanical phase transitions governing\u0000the properties of biological materials ranging from the cytoskeletons of cells\u0000to the extracellular networks of tissues such as tendon where the networks are\u0000often preferentially aligned.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Usually, the Carnot efficiency cannot be achieved with finite power due to the quasi-static process, which requires infinitely slow operation speed. It is necessary to tolerate extra dissipation to obtain finite power. In the slow-driving linear response regime, this dissipation can be described as dissipated availability in a geometrical way. The key to this geometrical method is the thermodynamic length characterized by a metric tensor defined on the space of control variables. In this paper, we show that the metric tensor for Langevin dynamics can be decomposed in terms of the relaxation times of a system. As an application of the decomposition of the metric tensor, we show that it is possible to achieve Carnot efficiency at finite power by taking the vanishing limit of relaxation times without breaking trade-off relations between efficiency and power.
{"title":"Decomposition of metric tensor in thermodynamic geometry in terms of relaxation timescales","authors":"Zhen Li, Yuki Izumida","doi":"arxiv-2409.08546","DOIUrl":"https://doi.org/arxiv-2409.08546","url":null,"abstract":"Usually, the Carnot efficiency cannot be achieved with finite power due to\u0000the quasi-static process, which requires infinitely slow operation speed. It is\u0000necessary to tolerate extra dissipation to obtain finite power. In the\u0000slow-driving linear response regime, this dissipation can be described as\u0000dissipated availability in a geometrical way. The key to this geometrical\u0000method is the thermodynamic length characterized by a metric tensor defined on\u0000the space of control variables. In this paper, we show that the metric tensor\u0000for Langevin dynamics can be decomposed in terms of the relaxation times of a\u0000system. As an application of the decomposition of the metric tensor, we show\u0000that it is possible to achieve Carnot efficiency at finite power by taking the\u0000vanishing limit of relaxation times without breaking trade-off relations\u0000between efficiency and power.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the quantum Newman-Moore model, or quantum triangular plaquette model (qTPM), in the presence of a longitudinal field (qTPMz). We present evidence that indicates that the ground state phase diagram of the qTPMz includes various frustrated phases breaking translational symmetries, dependent on the specific sequence of system sizes used to take the large-size limit. This phase diagram includes the known first-order phase transition of the qTPM, but also additional first-order transitions due to the frustrated phases. Using the average longitudinal magnetization as an order parameter, we analyze the magnetization plateaus that characterize the ground state phases, describe their degeneracies, and obtain the qTPMz phase diagram using classical transfer matrix and quantum matrix product state techniques. We identify a region of parameter space which can be effectively described by a Rydberg blockade model on the triangular lattice and also find indications of $mathbb{Z}_2$ topological order connecting the quantum paramagnetic and classical frustrated phases.
{"title":"The quantum Newman-Moore model in a longitudinal field","authors":"Konstantinos Sfairopoulos, Juan P. Garrahan","doi":"arxiv-2409.09235","DOIUrl":"https://doi.org/arxiv-2409.09235","url":null,"abstract":"We study the quantum Newman-Moore model, or quantum triangular plaquette\u0000model (qTPM), in the presence of a longitudinal field (qTPMz). We present\u0000evidence that indicates that the ground state phase diagram of the qTPMz\u0000includes various frustrated phases breaking translational symmetries, dependent\u0000on the specific sequence of system sizes used to take the large-size limit.\u0000This phase diagram includes the known first-order phase transition of the qTPM,\u0000but also additional first-order transitions due to the frustrated phases. Using\u0000the average longitudinal magnetization as an order parameter, we analyze the\u0000magnetization plateaus that characterize the ground state phases, describe\u0000their degeneracies, and obtain the qTPMz phase diagram using classical transfer\u0000matrix and quantum matrix product state techniques. We identify a region of\u0000parameter space which can be effectively described by a Rydberg blockade model\u0000on the triangular lattice and also find indications of $mathbb{Z}_2$\u0000topological order connecting the quantum paramagnetic and classical frustrated\u0000phases.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In thermal environments, information processing requires thermodynamic costs determined by the second law of thermodynamics. Information processing within finite time is particularly important, since fast information processing has practical significance but is inevitably accompanied by additional dissipation. In this paper, we reveal the fundamental thermodynamic costs and the tradeoff relations between incompatible information processing such as measurement and feedback in the finite-time regime. To this end, we generalize optimal transport theory so as to be applicable to subsystems such as the memory and the engine in Maxwell's demon setups. Specifically, we propose a general framework to derive the Pareto fronts of entropy productions and thermodynamic activities, and provide a geometrical perspective on their structure. In an illustrative example, we find that even in situations where naive optimization of total dissipation cannot realize the function of Maxwell's demon, reduction of the dissipation in the feedback system according to the tradeoff relation enables the realization of the demon. We also show that an optimal Maxwell's demon can be implemented by using double quantum dots. Our results would serve as a designing principle of efficient thermodynamic machines performing information processing, from single electron devices to biochemical signal transduction.
{"title":"Finite-time thermodynamic bounds and tradeoff relations for information processing","authors":"Takuya Kamijima, Ken Funo, Takahiro Sagawa","doi":"arxiv-2409.08606","DOIUrl":"https://doi.org/arxiv-2409.08606","url":null,"abstract":"In thermal environments, information processing requires thermodynamic costs\u0000determined by the second law of thermodynamics. Information processing within\u0000finite time is particularly important, since fast information processing has\u0000practical significance but is inevitably accompanied by additional dissipation.\u0000In this paper, we reveal the fundamental thermodynamic costs and the tradeoff\u0000relations between incompatible information processing such as measurement and\u0000feedback in the finite-time regime. To this end, we generalize optimal\u0000transport theory so as to be applicable to subsystems such as the memory and\u0000the engine in Maxwell's demon setups. Specifically, we propose a general\u0000framework to derive the Pareto fronts of entropy productions and thermodynamic\u0000activities, and provide a geometrical perspective on their structure. In an\u0000illustrative example, we find that even in situations where naive optimization\u0000of total dissipation cannot realize the function of Maxwell's demon, reduction\u0000of the dissipation in the feedback system according to the tradeoff relation\u0000enables the realization of the demon. We also show that an optimal Maxwell's\u0000demon can be implemented by using double quantum dots. Our results would serve\u0000as a designing principle of efficient thermodynamic machines performing\u0000information processing, from single electron devices to biochemical signal\u0000transduction.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The mean square displacement (MSD) of intruders (tracer particles) immersed in a multicomponent granular mixture made up of smooth inelastic hard spheres in a homogeneous cooling state is explicitly computed. The multicomponent granular mixture is constituted by $s$ species with different masses, diameters, and coefficients of restitution. In the hydrodynamic regime, the time decay of the granular temperature of the mixture gives rise to a time decay of the intruder's diffusion coefficient $D_0$. The corresponding MSD of the intruder is determined by integrating the corresponding diffusion equation. As expected from previous works on binary mixtures, we find a logarithmic time dependence of the MSD which involves the coefficient $D_0$. To analyze the dependence of the MSD on the parameter space of the system, the diffusion coefficient is explicitly determined by considering the so-called second Sonine approximation (two terms in the Sonine polynomial expansion of the intruder's distribution function). The theoretical results for $D_0$ are compared with those obtained by numerically solving the Boltzmann equation by means of the direct simulation Monte Carlo method. We show that the second Sonine approximation improves the predictions of the first Sonine approximation, especially when the intruders are much lighter than the particles of the granular mixture. In the long-time limit, our results for the MSD agree with those recently obtained by Bodrova [Phys. Rev. E textbf{109}, 024903 (2024)] when $D_0$ is determined by considering the first Sonine approximation.
{"title":"Mean square displacement of intruders in freely cooling multicomponent granular mixtures","authors":"Rubén Gómez González, Santos Bravo Yuste, Vicente Garzó","doi":"arxiv-2409.08726","DOIUrl":"https://doi.org/arxiv-2409.08726","url":null,"abstract":"The mean square displacement (MSD) of intruders (tracer particles) immersed\u0000in a multicomponent granular mixture made up of smooth inelastic hard spheres\u0000in a homogeneous cooling state is explicitly computed. The multicomponent\u0000granular mixture is constituted by $s$ species with different masses,\u0000diameters, and coefficients of restitution. In the hydrodynamic regime, the\u0000time decay of the granular temperature of the mixture gives rise to a time\u0000decay of the intruder's diffusion coefficient $D_0$. The corresponding MSD of\u0000the intruder is determined by integrating the corresponding diffusion equation.\u0000As expected from previous works on binary mixtures, we find a logarithmic time\u0000dependence of the MSD which involves the coefficient $D_0$. To analyze the\u0000dependence of the MSD on the parameter space of the system, the diffusion\u0000coefficient is explicitly determined by considering the so-called second Sonine\u0000approximation (two terms in the Sonine polynomial expansion of the intruder's\u0000distribution function). The theoretical results for $D_0$ are compared with\u0000those obtained by numerically solving the Boltzmann equation by means of the\u0000direct simulation Monte Carlo method. We show that the second Sonine\u0000approximation improves the predictions of the first Sonine approximation,\u0000especially when the intruders are much lighter than the particles of the\u0000granular mixture. In the long-time limit, our results for the MSD agree with\u0000those recently obtained by Bodrova [Phys. Rev. E textbf{109}, 024903 (2024)]\u0000when $D_0$ is determined by considering the first Sonine approximation.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"193 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tsuneya Yoshida, J. Lukas K. König, Lukas Rødland, Emil J. Bergholtz, Marcus Stålhammar
Despite their ubiquity, systematic characterization of multifold exceptional points, $n$-fold exceptional points (EP$n$s), remains a significant unsolved problem. In this article, we characterize Abelian topology of eigenvalues for generic EP$n$s and symmetry-protected EP$n$s for arbitrary $n$. The former and the latter emerge in a $(2n-2)$- and $(n-1)$-dimensional parameter space, respectively. By introducing resultant winding numbers, we elucidate that these EP$n$s are stable due to topology of a map from a base space (momentum or parameter space) to a sphere defined by these resultants. Our framework implies fundamental doubling theorems of both generic EP$n$s and symmetry-protected EP$n$s in $n$-band models.
{"title":"Winding Topology of Multifold Exceptional Points","authors":"Tsuneya Yoshida, J. Lukas K. König, Lukas Rødland, Emil J. Bergholtz, Marcus Stålhammar","doi":"arxiv-2409.09153","DOIUrl":"https://doi.org/arxiv-2409.09153","url":null,"abstract":"Despite their ubiquity, systematic characterization of multifold exceptional\u0000points, $n$-fold exceptional points (EP$n$s), remains a significant unsolved\u0000problem. In this article, we characterize Abelian topology of eigenvalues for\u0000generic EP$n$s and symmetry-protected EP$n$s for arbitrary $n$. The former and\u0000the latter emerge in a $(2n-2)$- and $(n-1)$-dimensional parameter space,\u0000respectively. By introducing resultant winding numbers, we elucidate that these\u0000EP$n$s are stable due to topology of a map from a base space (momentum or\u0000parameter space) to a sphere defined by these resultants. Our framework implies\u0000fundamental doubling theorems of both generic EP$n$s and symmetry-protected\u0000EP$n$s in $n$-band models.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Diffusion in complex heterogeneous media such as biological tissues or porous materials typically involves constrained displacements in tortuous structures and {em sticky} environments. Therefore, diffusing particles experience both entropic (excluded-volume) forces and the presence of complex energy landscapes. In this situation, one may describe transport through an effective diffusion coefficient. In this paper, we examine comb structures with finite-length 1D and finite-area 2D fingers, which act as purely diffusive traps. We find that there exists a critical width of 2D fingers above which the effective diffusion along the backbone is faster than for an equivalent arrangement of 1D fingers. Moreover, we show that the effective diffusion coefficient is described by a general analytical form for both 1D and 2D fingers, provided the correct scaling variable is identified as a function of the structural parameters. Interestingly, this formula corresponds to the well-known general situation of diffusion in a medium with fast reversible adsorption. Finally, we show that the same formula describes diffusion in the presence of dilute potential energy traps, e.g. through a landscape of square wells. While diffusion is ultimately always the results of microscopic interactions (with particles in the fluid, other solutes and the environment), effective representations are often of great practical use. The results reported in this paper help clarify the microscopic origins and the applicability of global, integrated descriptions of diffusion in complex media.
{"title":"Effective diffusion along the backbone of combs with finite-span 1D and 2D fingers","authors":"Giovanni Bettarini, Francesco Piazza","doi":"arxiv-2409.08855","DOIUrl":"https://doi.org/arxiv-2409.08855","url":null,"abstract":"Diffusion in complex heterogeneous media such as biological tissues or porous\u0000materials typically involves constrained displacements in tortuous structures\u0000and {em sticky} environments. Therefore, diffusing particles experience both\u0000entropic (excluded-volume) forces and the presence of complex energy\u0000landscapes. In this situation, one may describe transport through an effective\u0000diffusion coefficient. In this paper, we examine comb structures with\u0000finite-length 1D and finite-area 2D fingers, which act as purely diffusive\u0000traps. We find that there exists a critical width of 2D fingers above which the\u0000effective diffusion along the backbone is faster than for an equivalent\u0000arrangement of 1D fingers. Moreover, we show that the effective diffusion\u0000coefficient is described by a general analytical form for both 1D and 2D\u0000fingers, provided the correct scaling variable is identified as a function of\u0000the structural parameters. Interestingly, this formula corresponds to the\u0000well-known general situation of diffusion in a medium with fast reversible\u0000adsorption. Finally, we show that the same formula describes diffusion in the\u0000presence of dilute potential energy traps, e.g. through a landscape of square\u0000wells. While diffusion is ultimately always the results of microscopic\u0000interactions (with particles in the fluid, other solutes and the environment),\u0000effective representations are often of great practical use. The results\u0000reported in this paper help clarify the microscopic origins and the\u0000applicability of global, integrated descriptions of diffusion in complex media.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
P. Maynar, M. I. García de Soria, D. Guéry-Odelin, E. Trizac
The dynamics of a system composed of elastic hard particles confined by an isotropic harmonic potential are studied. In the low-density limit, the Boltzmann equation provides an excellent description, and the system does not reach equilibrium except for highly specific initial conditions: it generically evolves towards and stays in a breathing mode. This state is periodic in time, with a Gaussian velocity distribution, an oscillating temperature and a density profile that oscillates as well. We characterize this breather in terms of initial conditions, and constants of the motion. For low but finite densities, the analysis requires to take into account the finite size of the particles. Under well-controlle approximations, a closed description is provided, which shows how equilibrium is reached at long times. The (weak) dissipation at work erodes the breather's amplitude, while concomitantly shifting its oscillation frequency. An excellent agreement is found between Molecular Dynamics simulation results and the theoretical predictions for the frequency shift. For the damping time, the agreement is not as accurate as for the frequency and the origin of the discrepancies is discussed.
{"title":"Fate of Boltzmann's breathers: kinetic theory perspective","authors":"P. Maynar, M. I. García de Soria, D. Guéry-Odelin, E. Trizac","doi":"arxiv-2409.07831","DOIUrl":"https://doi.org/arxiv-2409.07831","url":null,"abstract":"The dynamics of a system composed of elastic hard particles confined by an\u0000isotropic harmonic potential are studied. In the low-density limit, the\u0000Boltzmann equation provides an excellent description, and the system does not\u0000reach equilibrium except for highly specific initial conditions: it generically\u0000evolves towards and stays in a breathing mode. This state is periodic in time,\u0000with a Gaussian velocity distribution, an oscillating temperature and a density\u0000profile that oscillates as well. We characterize this breather in terms of\u0000initial conditions, and constants of the motion. For low but finite densities,\u0000the analysis requires to take into account the finite size of the particles.\u0000Under well-controlle approximations, a closed description is provided, which\u0000shows how equilibrium is reached at long times. The (weak) dissipation at work\u0000erodes the breather's amplitude, while concomitantly shifting its oscillation\u0000frequency. An excellent agreement is found between Molecular Dynamics\u0000simulation results and the theoretical predictions for the frequency shift. For\u0000the damping time, the agreement is not as accurate as for the frequency and the\u0000origin of the discrepancies is discussed.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"187 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pablo Díez-Valle, Fernando Martínez-García, Juan José García-Ripoll, Diego Porras
We introduce a variational algorithm based on Matrix Product States that is trained by minimizing a generalized free energy defined using Tsallis entropy instead of the standard Gibbs entropy. As a result, our model can generate the probability distributions associated with generalized statistical mechanics. The resulting model can be efficiently trained, since the resulting free energy and its gradient can be calculated exactly through tensor network contractions, as opposed to standard methods which require estimating the Gibbs entropy by sampling. We devise a variational annealing scheme by ramping up the inverse temperature, which allows us to train the model while avoiding getting trapped in local minima. We show the validity of our approach in Ising spin-glass problems by comparing it to exact numerical results and quasi-exact analytical approximations. Our work opens up new possibilities for studying generalized statistical physics and solving combinatorial optimization problems with tensor networks.
{"title":"Learning Generalized Statistical Mechanics with Matrix Product States","authors":"Pablo Díez-Valle, Fernando Martínez-García, Juan José García-Ripoll, Diego Porras","doi":"arxiv-2409.08352","DOIUrl":"https://doi.org/arxiv-2409.08352","url":null,"abstract":"We introduce a variational algorithm based on Matrix Product States that is\u0000trained by minimizing a generalized free energy defined using Tsallis entropy\u0000instead of the standard Gibbs entropy. As a result, our model can generate the\u0000probability distributions associated with generalized statistical mechanics.\u0000The resulting model can be efficiently trained, since the resulting free energy\u0000and its gradient can be calculated exactly through tensor network contractions,\u0000as opposed to standard methods which require estimating the Gibbs entropy by\u0000sampling. We devise a variational annealing scheme by ramping up the inverse\u0000temperature, which allows us to train the model while avoiding getting trapped\u0000in local minima. We show the validity of our approach in Ising spin-glass\u0000problems by comparing it to exact numerical results and quasi-exact analytical\u0000approximations. Our work opens up new possibilities for studying generalized\u0000statistical physics and solving combinatorial optimization problems with tensor\u0000networks.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We numerically study zeroes of the partition function for trimers ($k = 3$) on $3 times L$ strip. While such results for dimers ($k = 2$) on 2D lattices are well known to always lie on the negative real axis and are unbounded, here we see that the zeroes are bounded on branches in a finite-sized region and with a considerable number of them being complex. We analyze this result further to numerically study the density of zeroes on such branches, estimating the critical power-law exponents, and make interesting observations on density of filled sites in the lattice as a function of activity $z$.
{"title":"A numerical study of the zeroes of the grand partition function of hard needles of length $k$ on stripes of width $k$","authors":"Soumyadeep Sarma","doi":"arxiv-2409.07744","DOIUrl":"https://doi.org/arxiv-2409.07744","url":null,"abstract":"We numerically study zeroes of the partition function for trimers ($k = 3$)\u0000on $3 times L$ strip. While such results for dimers ($k = 2$) on 2D lattices\u0000are well known to always lie on the negative real axis and are unbounded, here\u0000we see that the zeroes are bounded on branches in a finite-sized region and\u0000with a considerable number of them being complex. We analyze this result\u0000further to numerically study the density of zeroes on such branches, estimating\u0000the critical power-law exponents, and make interesting observations on density\u0000of filled sites in the lattice as a function of activity $z$.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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