On Zeros and Algorithms for Disordered Systems II: The Antiferromagnetic Ising Model up to Kesten-Stigum

Classés selon la proximité de leur titre et de leur résumé avec ceux de cet article. Sélectionnez-en pour les lire ensemble.

Les articles les plus proches

1. Très proche Contexte plus large Pas pertinent

   Computational thresholds for the fixed-magnetization Ising model

   Charles Carlson, Ewan Davies, Alexandra Kolla et al. · 2021 · Symposium on the Theory of Computing · cité 14 fois · Pas encore résumé

   Computational thresholds for the modèle ferromagnétique à magnétisation fixée étudie la difficulté du comptage et de l’échantillonnage, plutôt que l’approximation sur graphes aléatoires d-réguliers.

   Résumé scientifique

   The ferromagnetic Ising model is a model of a magnetic material and a central topic in statistical physics. It also plays a starring role in the algorithmic study of approximate counting: approximating the partition function of the ferromagnetic Ising model with uniform external field is tractable at all temperatures and on all graphs, due to the randomized algorithm of Jerrum and Sinclair. Here we show that hidden inside the model are hard computational problems. For the class of bounded-degree graphs we find computational thresholds for the approximate counting and sampling problems for the ferromagnetic Ising model at fixed magnetization (that is, fixing the number of +1 and −1 spins). In…

2. Proche Autre approche du problème Pas pertinent

   Approximation algorithms for the random-field Ising model

   Tyler Helmuth, Holden Lee, Will Perkins et al. · 2021 · SIAM Journal on Discrete Mathematics · cité 3 fois · Pas encore résumé

   Approximation algorithms for the random-field Ising model construit des schémas d’approximation et d’échantillonnage pour Ising ferromagnétique sous des champs gaussiens aléatoires.

   Résumé scientifique

   Approximating the partition function of the ferromagnetic Ising model with general external fields is known to be #BIS-hard in the worst case, even for bounded-degree graphs, and it is widely believed that no polynomial-time approximation scheme exists. This motivates an average-case question: are there classes of instances for which polynomial-time approximation schemes exist? We investigate this question for the random field Ising model on graphs with maximum degree $\Delta$. We establish the existence of fully polynomial-time approximation schemes and samplers with high probability over the random fields if the external fields are IID Gaussians with variance larger than a constant dependi…

3. Proche Autre approche du problème Pas pertinent

   Efficient Algorithms for Approximating Quantum Partition Functions

   Ryan L. Mann, Tyler Helmuth · 2020 · Journal of Mathematics and Physics · cité 30 fois · Pas encore résumé

   Efficient Algorithms for Approximating Quantum Partition Functions approche les fonctions de partition par développement en amas à haute température, pour des modèles quantiques.

   Résumé scientifique

   We establish a polynomial-time approximation algorithm for partition functions of quantum spin models at high temperature. Our algorithm is based on the quantum cluster expansion of Netocny and Redig and the cluster expansion approach to designing algorithms due to Helmuth, Perkins, and Regts. Similar results have previously been obtained by related methods, and our main contribution is a simple and slightly sharper analysis for the case of pairwise interactions on bounded-degree graphs.

4. Proche Contexte plus large Pas pertinent

   Sampling from the Potts model at low temperatures via Swendsen–Wang dynamics

   Antonio Blanca, Reza Gheissari · 2023 · IEEE Annual Symposium on Foundations of Computer Science · cité 7 fois · Pas encore résumé

   Sampling from the Potts model at low temperatures via Swendsen–Wang dynamics étudie l’échantillonnage du Potts ferromagnétique à basse température sur des graphes structurés.

   Résumé scientifique

   Sampling from the q-state ferromagnetic Potts model is a fundamental question in statistical physics, probability theory, and theoretical computer science. On general graphs, this problem is computationally hard, and this hardness holds at arbitrarily low temperatures. At the same time, in recent years, there has been significant progress showing the existence of low-temperature sampling algorithms in various specific families of graphs. Our aim in this paper is to understand the minimal structural properties of general graphs that enable polynomial-time sampling from the q-state ferromagnetic Potts model at low temperatures. We study this problem from the perspective of the widely-used Swen…

5. Proche Contexte plus large Pas pertinent

   On the tractability of sampling from the Potts model at low temperatures via random-cluster dynamics

   Antonio Blanca, Reza Gheissari · 2023 · Probability theory and related fields · cité 5 fois · Pas encore résumé

   On the tractability of sampling from the Potts model at low temperatures via random-cluster dynamics examine l’échantillonnage du Potts à basse température par une dynamique de amas aléatoires.

   Résumé scientifique

   Sampling from the q-state ferromagnetic Potts model is a fundamental question in statistical physics, probability theory, and theoretical computer science. On general graphs, this problem may be computationally hard, and this hardness holds at arbitrarily low temperatures. At the same time, in recent years, there has been significant progress showing the existence of low-temperature sampling algorithms in various specific families of graphs. Our aim in this paper is to understand the minimal structural properties of general graphs that enable polynomial-time sampling from the q-state ferromagnetic Potts model at low temperatures. We study this problem from the perspective of random-cluster d…

6. Proche Même question Pas pertinent

   The complexity of approximating the complex-valued Ising model on bounded degree graphs

   Andreas Galanis, L. Goldberg, Andrés Herrera-Poyatos · 2021 · SIAM Journal on Discrete Mathematics · cité 10 fois · Pas encore résumé

   The complexity of approximating the complex-valued Ising model on bounded degree graphs analyse la complexité d’approximation de la fonction de partition d’Ising pour des interactions complexes.

   Résumé scientifique

   We study the complexity of approximating the partition function $Z_{\mathrm{Ising}}(G; \beta)$ of the Ising model in terms of the relation between the edge interaction $\beta$ and a parameter $\Delta$ which is an upper bound on the maximum degree of the input graph $G$. Following recent trends in both statistical physics and algorithmic research, we allow the edge interaction $\beta$ to be any complex number. Many recent partition function results focus on complex parameters, both because of physical relevance and because of the key role of the complex case in delineating the tractability/intractability phase transition of the approximation problem. In this work we establish both new tractab…

7. Proche Même méthode, autre problème Pas pertinent

   Finite-size scaling, phase coexistence, and algorithms for the random cluster model on random graphs

   Tyler Helmuth, Matthew Jenssen, Will Perkins · 2020 · Annales De L Institut Henri Poincare-probabilites Et Statistiques · cité 34 fois · Pas encore résumé

   Finite-size scaling, phase coexistence, and algorithms for the random cluster model on random graphs utilise modèles polymères et développement en amas pour compter et échantillonner sur graphes réguliers aléatoires.

   Résumé scientifique

   For $\Delta \ge 5$ and $q$ large as a function of $\Delta$, we give a detailed picture of the phase transition of the random cluster model on random $\Delta$-regular graphs. In particular, we determine the limiting distribution of the weights of the ordered and disordered phases at criticality and prove exponential decay of correlations away from criticality. Our techniques are based on using polymer models and the cluster expansion to control deviations from the ordered and disordered ground states. These techniques also yield efficient approximate counting and sampling algorithms for the Potts and random cluster models on random $\Delta$-regular graphs at all temperatures when $q$ is large…

8. Proche Contexte plus large Pas pertinent

   Exact Fractional Inference via Re-Parametrization & Interpolation between Tree-Re-Weighted- and Belief Propagation- Algorithms

   Hamidreza Behjoo, M. Chertkov · 2023 · Trans. Mach. Learn. Res. · cité 1 fois · Pas encore résumé

   Exact Fractional Inference via Re-Parametrization & Interpolation between Tree-Re-Weighted- and Belief Propagation- Algorithms propose une approximation variationnelle de la fonction de partition d’Ising.

   Résumé scientifique

   Computing the partition function, $Z$, of an Ising model over a graph of $N$ \enquote{spins} is most likely exponential in $N$. Efficient variational methods, such as Belief Propagation (BP) and Tree Re-Weighted (TRW) algorithms, compute $Z$ approximately by minimizing the respective (BP- or TRW-) free energy. We generalize the variational scheme by building a $\lambda$-fractional interpolation, $Z^{(\lambda)}$, where $\lambda=0$ and $\lambda=1$ correspond to TRW- and BP-approximations, respectively. This fractional scheme -- coined Fractional Belief Propagation (FBP) -- guarantees that in the attractive (ferromagnetic) case $Z^{(TRW)} \geq Z^{(\lambda)} \geq Z^{(BP)}$, and there exists a un…