Journal of Statistical Physics最新文献

{"title":"Rigorous Lower Bound of the Dynamical Critical Exponent of the Ising Model","authors":"Rintaro Masaoka,&nbsp;Tomohiro Soejima,&nbsp;Haruki Watanabe","doi":"10.1007/s10955-025-03456-3","DOIUrl":"10.1007/s10955-025-03456-3","url":null,"abstract":"<div><p>We study the kinetic Ising model under Glauber dynamics and establish an upper bound on the spectral gap for finite systems. This bound implies the critical exponent inequality <span>(z ge 2)</span>, thereby rigorously improving the previously known estimate <span>(z ge 2 - eta )</span>. Our proof relies on the mapping from stochastic processes to frustration-free quantum systems and leverages the Simon–Lieb and Gosset–Huang inequalities.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03456-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144135390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Green’s Function Perspective on the Nonlinear Density Response of Quantum Many-Body Systems","authors":"Jan Vorberger,&nbsp;Tobias Dornheim,&nbsp;Maximilian P. Böhme,&nbsp;Zhandos A. Moldabekov,&nbsp;Panagiotis Tolias","doi":"10.1007/s10955-025-03454-5","DOIUrl":"10.1007/s10955-025-03454-5","url":null,"abstract":"<div><p>We derive equations of motion for higher order density response functions using the theory of thermodynamic Green’s functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions. Moreover, we relate higher order response functions and higher order collision integrals within the Martin–Schwinger hierarchy. We expect our results to be highly relevant to the study of a variety of quantum many-body systems such as matter under extreme temperatures, densities, and pressures.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03454-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144131488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Path Method for Non-exponential Ergodicity of Markov Chains and Its Application for Chemical Reaction Systems","authors":"Minjun Kim,&nbsp;Jinsu Kim","doi":"10.1007/s10955-025-03453-6","DOIUrl":"10.1007/s10955-025-03453-6","url":null,"abstract":"<div><p>In this paper, we present criteria for non-exponential ergodicity of continuous-time Markov chains on a countable state space in total variation norm. These criteria can be verified by examining the ratio of transition rates over certain paths. We applied this path method to explore the non-exponential convergence of microscopic biochemical interacting systems. Using reaction network descriptions, we identified special architectures of biochemical systems for non-exponential ergodicity. In essence, we found that reactions forming a cycle in the reaction network can induce non-exponential ergodicity when they significantly dominate other reactions across infinitely many regions of the state space. Interestingly, the special architectures allowed us to construct many detailed balanced and complex balanced biochemical systems that are non-exponentially ergodic. Some of these models are low-dimensional bimolecular systems with few reactions. Thus this work suggests the possibility of discovering or synthesizing stochastic systems arising in biochemistry that possess either detailed balancing or complex balancing and slowly converge to their stationary distribution.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144125520","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}

{"title":"Polynomial Escape Rates via Maximal Large Deviations","authors":"Yaofeng Su","doi":"10.1007/s10955-025-03455-4","DOIUrl":"10.1007/s10955-025-03455-4","url":null,"abstract":"<div><p>In this short note, we propose a new and short approach to polynomial escape rates, which can be applied to various open systems with intermittency. The tool of our approach is the maximal large deviations developed in [5].</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03455-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143949655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exact Calculation of the Large Deviation Function for k-nary Coalescence","authors":"R. Rajesh,&nbsp;V. Subashri,&nbsp;Oleg Zaboronski","doi":"10.1007/s10955-025-03412-1","DOIUrl":"10.1007/s10955-025-03412-1","url":null,"abstract":"<div><p>We study probabilities of rare events in the general coalescence process, <span>(kArightarrow ell A)</span>, where <span>(k&gt;ell )</span>. For arbitrary <span>(k, ell )</span>, by rewriting these probabilities in terms of an effective action, we derive the large deviation function describing the probability of finding <i>N</i> particles at time <i>t</i>, when starting with <i>M</i> particles initially. Additionally, the most probable trajectory corresponding to a fixed rare event is derived.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03412-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143932330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Large-Deviation Analysis for Canonical Gibbs Measures","authors":"Christian Hirsch,&nbsp;Martina Petráková","doi":"10.1007/s10955-025-03451-8","DOIUrl":"10.1007/s10955-025-03451-8","url":null,"abstract":"<div><p>In this paper, we present a large-deviation theory developed for functionals of canonical Gibbs processes, i.e., Gibbs processes with respect to the binomial point process. We study the regime of a fixed intensity in a sequence of increasing windows. Our method relies on the traditional large-deviation result for local bounded functionals of Poisson point processes noting that the binomial point process is obtained from the Poisson point process by conditioning on the point number. Our main methodological contribution is the development of coupling constructions allowing us to handle delicate and unlikely pathological events. The presented results cover three types of Gibbs models — a model given by a bounded local interaction, a model given by a non-negative possibly unbounded increasing local interaction and the hard-core interaction model. The derived large deviation principle is formulated for the distributions of individual empirical fields driven by canonical Gibbs processes, with its special case being a large deviation principle for local bounded observables of the canonical Gibbs processes. We also consider unbounded non-negative increasing local observables, but the price for treating this more general case is that we only get large-deviation bounds for the tails of such observables. Our primary setting is the one with periodic boundary condition, however, we also discuss generalizations for different choices of the boundary condition.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03451-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143919034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Scale-dependent elasticity as a probe of universal heterogeneity in equilibrium amorphous solids","authors":"Boli Zhou,&nbsp;Rafael Hipolito,&nbsp;Paul M. Goldbart","doi":"10.1007/s10955-025-03450-9","DOIUrl":"10.1007/s10955-025-03450-9","url":null,"abstract":"<div><p>The equilibrium amorphous solid state—formed, <i>e.g.</i>, by adequately randomly crosslinking the constituents of a macromolecular fluid—is a heterogeneous state characterized by a universal distribution of particle localization lengths. Near to the crosslink-density-controlled continuous amorphous-solidification transition, this distribution obeys a scaling form: it has a single peak at a lengthscale that diverges (along with the width of the distribution) as the transition is approached. The modulus controlling macroscale elastic shear deformations of the amorphous solid does not depend on the distribution of localization lengths. However, it is natural to anticipate that for deformations at progressively shorter lengthscales—mesoscale deformations—the effective modulus exhibits a scale-dependence, softening as the deformation lengthscale is reduced. This is because an increasing fraction of the localized particles are, in effect, liquid-like at the deformation lengthscale, and therefore less effective at contributing to the elastic response. In this Paper, the relationship between the distribution of localization lengths and the scale-dependent elastic shear modulus is explored. Following a discussion of intuitive expectations for the scale-dependent elasticity in the amorphous solid state, it is shown, within the setting of a replica mean-field theory, that the effective modulus does indeed exhibit scale-dependent softening. Through this softening, mesoscale elasticity provides a probe of the heterogeneity of the state as characterized by the distribution of localization lengths. In particular, the response to short-lengthscale elastic deformations is shown to shed light on the behavior of the universal localization-length distribution at short localization lengths. Certain experimental techniques that have the potential to yield information specifically about the mesoscale structure and elasticity of amorphous solid states are discussed.\u0000</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03450-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Radius of a Self-repelling Star Polymer","authors":"Carl Mueller,&nbsp;Eyal Neuman","doi":"10.1007/s10955-025-03444-7","DOIUrl":"10.1007/s10955-025-03444-7","url":null,"abstract":"<div><p>We study the effective radius of weakly self-avoiding star polymers in one, two, and three dimensions. Our model includes <i>N</i> Brownian motions up to time <i>T</i>, started at the origin and subject to exponential penalization based on the amount of time they spend close to each other, or close to themselves. The effective radius measures the typical distance from the origin. Our main result gives estimates for the effective radius where in two and three dimensions we impose the restriction that <span>(T le N)</span>. One of the highlights of our results is that in two dimensions, we find that the radius is proportional to <span>(T^{3/4})</span>, up to logarithmic corrections.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03444-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bounds on (T_c) in the Eliashberg Theory of Superconductivity. I: The (gamma )-Model","authors":"M. K.-H. Kiessling,&nbsp;B. L. Altshuler,&nbsp;E. A. Yuzbashyan","doi":"10.1007/s10955-025-03446-5","DOIUrl":"10.1007/s10955-025-03446-5","url":null,"abstract":"<div><p>Using the recent reformulation for the Eliashberg theory of superconductivity in terms of a classical interacting Bloch spin chain model, rigorous upper and lower bounds on the critical temperature <span>(T_c)</span> are obtained for the <span>(gamma )</span> model—a version of Eliashberg theory in which the effective electron–electron interaction is proportional to <span>((g/|omega _n-omega _m|)^{gamma })</span>, where <span>(omega _n-omega _m)</span> is the transferred Matsubara frequency, <span>(g&gt;0)</span> a reference energy, and <span>(gamma &gt;0)</span> a parameter. The rigorous lower bounds are based on a variational principle that identifies <span>((2pi T_c/g)^gamma )</span> with the largest (positive) eigenvalue <span>(mathfrak {g}(gamma ))</span> of an explicitly constructed compact, self-adjoint operator <span>(mathfrak {G}(gamma ))</span>. These lower bounds form an increasing sequence that converges to <span>(T_c(g,gamma ))</span>. The upper bound on <span>(T_c(g,gamma ))</span> is based on fixed point theory, proving linear stability of the normal state for <i>T</i> larger than the upper bound on <span>(T_c(g,gamma ))</span>.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03446-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analytical Methods for Continuous Attractor Neural Networks","authors":"Martino Salomone Centonze,&nbsp;Alessandro Treves,&nbsp;Elena Agliari,&nbsp;Adriano Barra","doi":"10.1007/s10955-025-03447-4","DOIUrl":"10.1007/s10955-025-03447-4","url":null,"abstract":"<div><p>Pyramidal cells that emit spikes when the animal is at specific locations of the environment are known as <i>place cells</i>: these neurons are thought to provide an internal representation of space via <i>cognitive maps</i>. Here, we consider the Battaglia-Treves neural network model for cognitive map storage and reconstruction, instantiated with McCulloch &amp; Pitts binary neurons. To quantify the information processing capabilities of these networks, we exploit spin-glass techniques, namely the <i>interpolation method</i> and the <i>replica trick</i>. In particular, in the low-storage regime (i.e., when the number of stored maps scales sub-linearly with the network size and the order parameters self-average around their means), by adapting the Hamilton-Jacobi PDE-approach, we obtain an exact phase diagram in the noise vs inhibition strength plane. In the high-storage regime, by adapting the standard interpolation based on stochastic stability, we find that—for mild inhibition and not too high noise—memorization and retrieval of an extensive number of spatial maps is possible. These results, holding under the replica-symmetry assumption, are recovered, for completeness, also by the replica method and they are corroborated by Monte Carlo simulations. Finally, by leveraging the integral representation of the model (in terms of a bipartite network equipped with highly-selective hidden units), we successfully test its robustness versus various distributions of place fields, including the log-normal distribution observed in recent experiments on bats navigating long tunnels. Additionally, we demonstrate that, by appropriately coupling these hidden units, the network can effectively orient itself even in dynamic environments.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03447-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143900662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}