Approximating partition functions of the two-state spin system

DOI10.1016/j.ipl.2011.04.012zbMath1260.68469OpenAlexW2162365350MaRDI QIDQ1944117

Yanyan Li

Publication date: 4 April 2013

Published in: Information Processing Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ipl.2011.04.012

zbMATH Keywords

Ising modelGibbs measureapproximation algorithmsFPTASstrong correlation decaytwo-state spin systemuniqueness of Gibbs measure

Mathematics Subject Classification ID

Applications of graph theory (05C90) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Approximation algorithms (68W25)

Related Items (18)

Rapid Mixing of Glauber Dynamics up to Uniqueness via Contraction ⋮ Zero-freeness and approximation of real Boolean Holant problems ⋮ Complexity of Ising Polynomials ⋮ Perfect Sampling in Infinite Spin Systems Via Strong Spatial Mixing ⋮ Exact thresholds for Ising-Gibbs samplers on general graphs ⋮ Approximation Algorithms for the Random Field Ising Model ⋮ Unnamed Item ⋮ Inapproximability of the Partition Function for the Antiferromagnetic Ising and Hard-Core Models ⋮ The Ising partition function: zeros and deterministic approximation ⋮ Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs ⋮ Fisher zeros and correlation decay in the Ising model ⋮ Sampling in Uniqueness from the Potts and Random-Cluster Models on Random Regular Graphs ⋮ Contraction: a unified perspective of correlation decay and zero-freeness of 2-spin systems ⋮ Fisher Zeros and Correlation Decay in the Ising Model ⋮ More on zeros and approximation of the Ising partition function ⋮ Spectral Independence in High-Dimensional Expanders and Applications to the Hardcore Model ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

• Ising models on locally tree-like graphs
• Gibbs measures and phase transitions
• Uniqueness of uniform random colorings of regular trees
• The Ising model and percolation on trees and tree-like graphs
• The critical Ising model on trees, concave recursions and nonlinear capacity
• Counting independent sets up to the tree threshold
• Rapid mixing of Gibbs sampling on graphs that are sparse on average
• Polynomial-Time Approximation Algorithms for the Ising Model
• Counting without sampling: Asymptotics of the log-partition function for certain statistical physics models
• The computational complexity of two‐state spin systems
• Prescribing a System of Random Variables by Conditional Distributions
• Combinatorial criteria for uniqueness of Gibbs measures

This page was built for publication: Approximating partition functions of the two-state spin system