Comparison of Swendsen-Wang and heat-bath dynamics

DOI10.1002/rsa.20431zbMath1272.82009arXiv1105.3665OpenAlexW3122801050MaRDI QIDQ2841682

Mario Ullrich

Publication date: 26 July 2013

Published in: Random Structures & Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.3665

zbMATH Keywords

spectral gapheat-bathIsing/Potts modelSwendsen-Wang

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Critical phenomena in equilibrium statistical mechanics (82B27) Coloring of graphs and hypergraphs (05C15)

Related Items (14)

Sampling Algorithms for Discrete Markov Random Fields and Related Graphical Models ⋮ Random-cluster dynamics in \(\mathbb {Z}^2\) ⋮ Random cluster dynamics for the Ising model is rapidly mixing ⋮ Hit-and-Run for Numerical Integration ⋮ The effect of boundary conditions on mixing of 2D Potts models at discontinuous phase transitions ⋮ Exponentially slow mixing in the mean-field Swendsen-Wang dynamics ⋮ Random-cluster dynamics in \(\mathbb{Z}^2\): rapid mixing with general boundary conditions ⋮ Efficient sampling and counting algorithms for the Potts model on ℤ^d at all temperatures ⋮ Cutoff for the Swendsen-Wang dynamics on the lattice ⋮ Unnamed Item ⋮ The worm process for the Ising model is rapidly mixing ⋮ Tunneling behavior of Ising and Potts models in the low-temperature regime ⋮ Random-cluster dynamics on random regular graphs in tree uniqueness ⋮ Rapid mixing of Swendsen–Wang dynamics in two dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Critical Ising on the square lattice mixes in polynomial time
• On the mixing time of the 2D stochastic Ising model with ``Plus boundary conditions at low temperature
• Dynamical analysis of low-temperature Monte Carlo cluster algorithms
• Comparison theorems for reversible Markov chains
• Approach to equilibrium of Glauber dynamics in the one phase region. I: The attractive case
• For 2-D lattice spin systems weak mixing implies strong mixing
• On weak mixing in lattice models
• Glauber dynamics on trees and hyperbolic graphs
• Tight bounds for mixing of the Swendsen-Wang algorithm at the Potts transition point
• Logarithmic Sobolev inequalities for finite Markov chains
• Mixing properties of the Swendsen–Wang process on the complete graph and narrow grids
• Probability on Graphs
• A bounding chain for Swendsen-Wang

This page was built for publication: Comparison of Swendsen-Wang and heat-bath dynamics