Journal of Statistical Physics最新文献

{"title":"Ising Model on Preferential Attachment Models","authors":"Remco van der Hofstad,&nbsp;Rounak Ray","doi":"10.1007/s10955-026-03674-3","DOIUrl":"10.1007/s10955-026-03674-3","url":null,"abstract":"<div><p>We study the Ising model on affine preferential attachment models with general parameters. We identify the thermodynamic limit of several quantities, arising in the large graph limit, such as pressure per particle, magnetisation, and internal energy for these models. Furthermore, we determine the inverse critical temperature for preferential attachment models (non-tree versions), showing that it equals zero in a certain parameter regime, while admitting an explicit closed-form expression in terms of the model parameters otherwise. Our proof for the thermodynamic limit of pressure per particle critically relies on the belief propagation theory for factor models on locally tree-like graphs, as developed by Dembo, Montanari, and Sun. It has been proved that preferential attachment models admit the Pólya point tree as their local limit under general conditions. We use the explicit characterisation of the Pólya point tree and belief propagation for factor models to obtain the explicit expression for the thermodynamic limit of the pressure per particle. Next, we use the convexity properties of the internal energy and magnetisation to determine their thermodynamic limits. To study the phase transition, we prove that the inverse critical temperature for a sequence of graphs and its local limit are equal. Finally, we show that the inverse critical temperature for the Pólya point tree admits an explicit closed-form expression in terms of the model parameters, using results from Lyons who shows that the critical inverse temperature is closely related to the percolation critical threshold. This part of the proof heavily relies on the critical percolation threshold for Pólya point trees established earlier with Hazra.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 11","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149338502","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":"A Coding-Theoretic Carnot Cycle: Extremal D-ary Huffman Bounds, the Sagawa–Ueda Identity, and a Closed-Form Efficiency","authors":"Pablo Garcia Tello","doi":"10.1007/s10955-026-03726-8","DOIUrl":"10.1007/s10955-026-03726-8","url":null,"abstract":"<div><p>We construct an exact, closed-form Carnot cycle whose state space is the simplex of probability distributions on a finite source alphabet, and whose working fluid is the optimal <i>D</i>-ary Huffman code attached to that source. The hot reservoir is identified with the uniform distribution, which maximises the average codeword length over all sources on a given alphabet; the cold reservoir is identified with a dominant-symbol quasi-uniform family whose average codeword length approaches its minimum possible value from above as the rare-symbol probability vanishes. Two adiabatic legs, defined by transcodings that preserve the dominant symbol’s unit-length codeword, close the cycle at a work cost that vanishes in the cold-reservoir limit. The resulting efficiency, expressed as the ratio of hot- to cold-reservoir temperatures in units of average codeword length, takes a closed form determined entirely by the alphabet sizes of the hot reservoir, and reproduces standard special cases including a value of eighty-seven and a half per cent for a binary source with two hundred and fifty-six symbols. We then embed the cycle in the Sagawa–Ueda generalised Jarzynski framework, identifying the trajectory-level mutual information with the log-likelihood difference between the source distribution and the codebook’s implicit distribution. Pathwise saturation of the resulting Jensen inequality is shown to require both source uniformity on its support and a matched codebook— a condition strictly stronger than the zero Kullback–Leibler criterion previously invoked in the literature. We derive the leading finite correction to the efficiency and show that it is linear in the rare-symbol weight, whereas the Jensen gap vanishes more slowly, so that pathwise saturation is restored before the Carnot limit is attained. The strict impossibility of reaching average codeword length equal to one for any source with more symbols than codeword letters is reinterpreted as a quantitative, third-law-style unattainability principle. The construction is exact at every step, is internally consistent with the Sagawa–Ueda framework, and closes rigorously the geometric Carnot diagram proposed in earlier work.\u0000</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 11","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03726-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149338276","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":"Quasicrystalline Gibbs States in 4-Dimensional Lattice-Gas Models with Finite-Range Interactions","authors":"Jacek Miȩkisz,&nbsp;Siamak Taati","doi":"10.1007/s10955-026-03727-7","DOIUrl":"10.1007/s10955-026-03727-7","url":null,"abstract":"<div><p>We construct a four-dimensional lattice-gas model with finite-range interactions that has non-periodic, “quasicrystalline” Gibbs states at low temperatures. Such Gibbs states are probability measures which are small perturbations of non-periodic ground-state configurations corresponding to stacked tilings of the plane with Ammann’s aperiodic tiles. Our construction is based on the correspondence between probabilistic cellular automata and Gibbs measures on their space-time trajectories, and a classical result on noise-resilient computing with cellular automata. The cellular automaton is constructed on the basis of Ammann’s tiles, which are deterministic in one direction, and has non-periodic space-time trajectories corresponding to each valid tiling. Repetitions along two extra dimensions, together with an error-correction mechanism based on Toom’s model, ensure stability of the trajectories in the presence of noise.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 11","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03727-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149338277","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":"Resonant Interactions in the (alpha )-FPUT Lattice with Site-Dependent Coefficients","authors":"Lorenzo Migliorelli,&nbsp;Giovanni Dematteis,&nbsp;Sergio Chibbaro,&nbsp;Miguel Onorato","doi":"10.1007/s10955-026-03724-w","DOIUrl":"10.1007/s10955-026-03724-w","url":null,"abstract":"<div><p>The wave turbulence framework has proven to be an effective tool for analyzing certain features of nonlinear energy transfer in one-dimensional nonlinear chains. In this work, we extend this approach to the <span>(alpha )</span>-FPUT problem when the spring stiffness <span>(chi )</span> and the nonlinear coefficient <span>(alpha )</span> are site-dependent. Although three-wave interactions are non-resonant for constant coefficients, their spatial modulation gives rise to a non-trivial resonant manifold. In this framework, we derive a new kinetic equation that suggests the possibility of substantially faster thermalization than in the constant-coefficient case. The new kinetic equation also includes an additional term that can be associated with the Bragg-scattering mechanism, which promotes the isotropization of the wave-action spectral density function. We corroborate these results with direct numerical simulations, confirming the radically faster thermalization pathway in the presence of random coefficients.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 11","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13731457/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149332019","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 Finite-Size Correction to the Minimal Height Probability in 2D Abelian Sandpiles","authors":"Miles W. Elvidge,&nbsp;Antal A. Járai","doi":"10.1007/s10955-026-03725-9","DOIUrl":"10.1007/s10955-026-03725-9","url":null,"abstract":"<div><p>We study the extent of universality in the finite-size scaling function for the probability of minimal height in the stationary Abelian sandpile on lattice approximations of a region <span>(U subset mathbb {C})</span> with lattice spacing <span>(varepsilon )</span> and with open boundary conditions. We show that under certain symmetry assumptions on the lattice, in the scaling limit <span>(varepsilon rightarrow 0)</span> this probability at a point <span>(z in U)</span> equals <span>(p_mathcal {G}(0) + varepsilon ^2 c_mathcal {G}f_U(z) + O(varepsilon ^3))</span>, where <span>(p_mathcal {G}(0))</span> is the height 0 probability on the full lattice, <span>(c_mathcal {G}&gt; 0)</span> is a constant depending only on the lattice, and <span>(f_U)</span> is a conformally covariant positive real-valued function depending only on <i>U</i>. This generalises a result of Brankov et al. [1], who considered the square lattice and the upper half plane. It also generalizes Example 4.10 in the recent study of the fermionic DGFF of Adame-Carillo and Ruszel [2]. We show via counterexamples that our symmetry assumption cannot be omitted, although conformal covariance may be recovered via an unusual scaling. In particular, the natural analogue of our result fails on general isoradial graphs. Our work is motivated by Jeng et al. [3], who computed the correction terms for all height variables in the special case of the upper half plane in <span>(mathbb {Z}^2)</span>. They conjectured that their results hold more generally and the present paper is a step in an attempt to make this conjecture rigorous.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 11","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03725-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149339266","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":"Growth Models Under Uniform Catastrophes","authors":"Joan Amaya,&nbsp;Valdivino V. Junior,&nbsp;Fábio P. Machado,&nbsp;Alejandro Roldán-Correa","doi":"10.1007/s10955-026-03718-8","DOIUrl":"10.1007/s10955-026-03718-8","url":null,"abstract":"<div><p>We consider stochastic growth models for populations organized in colonies and subject to uniform catastrophes. To assess population viability, we analyze scenarios in which individuals adopt dispersion strategies after catastrophic events. For these models, we derive explicit expressions for the survival probability and the mean time to extinction, both with and without spatial constraints. In addition, we complement this analysis by comparing uniform catastrophes with binomial and geometric catastrophes in models with dispersion and no spatial restrictions. Here, the terms uniform, binomial and geometric refer to the probability distributions governing the number of individuals that survive immediately after a catastrophe. This comparison allows us to quantify the impact of different types of catastrophic events on population persistence.\u0000</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 11","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03718-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149339170","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 Maximal Hard-Core Model as a Recoverable System: Gibbs Measures and Phase Coexistence","authors":"Geyang Wang,&nbsp;Alexander Barg,&nbsp;Navin Kashyap","doi":"10.1007/s10955-026-03716-w","DOIUrl":"10.1007/s10955-026-03716-w","url":null,"abstract":"<div><p>Recoverable systems provide coarse models of data storage on the two-dimensional square lattice <span>({mathbb Z}^2)</span>. In a recoverable system, each lattice site stores one bit of data, and the overall configuration of bits on the lattice is such that each site can reconstruct the value from its neighbors’ values according to a specified local rule. We initiate a study of such systems through the lens of statistical models for interacting bits on the <span>({mathbb Z}^2)</span> lattice. We consider two statistical models: (a) an interaction model with a temperature parameter that encourages configurations that respect the local recovery rule, and (b) a hard-core model with an activity parameter, supported only on the admissible configurations of the recoverable system. In this paper, we specifically study the recoverable system in which the admissible configurations are precisely those whose supports form maximal independent sets in the lattice. For the interaction model, we establish uniqueness of the Gibbs measure at high temperature and derive bounds on the entropy in the zero- and low-temperature regimes. For the hard-core model of maximal independent sets, we show phase coexistence at high activity. Unlike the standard hard-core model, however, the maximal version admits nontrivial ground states even at low activity, and we manage to classify them explicitly. We further verify the Peierls condition for appropriately defined contours. Combined with the Pirogov—Sinai theory, this shows that each ground state gives rise to an extremal Gibbs measure, proving phase coexistence at low activity.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 11","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149234309","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":"Order by Disorder up to Arbitrarily High Temperature","authors":"Ravish Mehta,&nbsp;Wojciech De Roeck","doi":"10.1007/s10955-026-03708-w","DOIUrl":"10.1007/s10955-026-03708-w","url":null,"abstract":"<div><p>We prove that a class of classical lattice models on <span>(mathbb {Z}^d)</span> (<span>(d ge 2)</span>) with on-site space <span>(mathbb {N}_0)</span> and nearest neighbour interaction exhibits long-range checkerboard order at sufficiently high temperature. The ordering mechanism is purely entropic. The class of models contains the recently introduced model of Han et al. [1], by which our work is inspired. The proof uses Pirogov–Sinai theory and the key input is a Peierls bound.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 11","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149234485","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":"Decay of the Survival Probability of a Local Excitation in Multi-qubit Platforms","authors":"Paolo Muratore-Ginanneschi,&nbsp;Bayan Karimi,&nbsp;Jukka Pekola","doi":"10.1007/s10955-026-03717-9","DOIUrl":"10.1007/s10955-026-03717-9","url":null,"abstract":"<div><p>We present a theoretical study of the survival probability of a state initially prepared in the one-particle sector of a multi-qubit system. The motivation for our work is the ongoing laboratory development of multi-qubit platforms based on superconducting circuits. Using elementary concepts of random matrix theory, we obtain analytic expressions for the survival probability in mathematical models of platforms which, albeit stylized, have been previously shown to provide relevant benchmarks for experimental data. In particular, we show that the decay properties are sensitive to the property of the Hamilton operator to have extended states. The survival probability does not appear instead to depend on whether the interaction between qubits is described by a Gaussian orthogonal ensemble (often interpreted as a model of “chaotic” dynamics) or is modeled by an analytically solvable chain. We interpret this phenomenon as a manifestation of a general mechanism for the emergence of equilibration in purely unitary dynamics. Finally, under the same hypothesis of an initial preparation with projection on a large fraction of the extended eigenstates of the Hamilton operator, we show how to extend the classical Kac–Mazur–Montroll estimate of the return time to the quantum survival probability.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 11","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03717-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149234486","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":"Persistence Probabilities for MA(1) Sequences with Uniform Innovations","authors":"Frank Aurzada,&nbsp;Kilian Raschel","doi":"10.1007/s10955-026-03720-0","DOIUrl":"10.1007/s10955-026-03720-0","url":null,"abstract":"<div><p>We study the persistence probabilities of a moving average process of order one with uniform innovations. We identify a number of regions—characterized by the location of the uniform distribution and the coupling parameter of the process—where the persistence probabilities have qualitatively different behaviour. We obtain the generating functions of the persistence probabilities explicitly in all possible regions. In some of the regions, the persistence probabilities can be expressed explicitly in terms of various combinatorial quantities.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 11","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189982","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}