Random-cluster dynamics in \(\mathbb{Z}^2\): rapid mixing with general boundary conditions

DOI10.1214/19-AAP1505zbMath1434.60273arXiv1807.08722OpenAlexW3006848352MaRDI QIDQ2180389

Reza Gheissari, Eric Vigoda, Antonio Blanca

Publication date: 13 May 2020

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.08722

zbMATH Keywords

Glauber dynamicsmixing timerandom-cluster modelspatial mixing

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (8)

The critical mean-field Chayes–Machta dynamics ⋮ Entropy decay in the Swendsen-Wang dynamics on \(\mathbb{Z}^d\) ⋮ The Swendsen–Wang dynamics on trees ⋮ Spatial mixing and the random‐cluster dynamics on lattices ⋮ Low-temperature Ising dynamics with random initializations ⋮ Unnamed Item ⋮ Sampling from Potts on random graphs of unbounded degree via random-cluster dynamics ⋮ Random-cluster dynamics on random regular graphs in tree uniqueness

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The phase transitions of the planar random-cluster and Potts models with \(q \geq 1\) are sharp
• Continuity of the phase transition for planar random-cluster and Potts models with \({1 \leq q \leq 4}\)
• The self-dual point of the two-dimensional random-cluster model is critical for \(q \geqslant 1\)
• On the mixing time of the 2D stochastic Ising model with ``Plus boundary conditions at low temperature
• For 2-D lattice spin systems weak mixing implies strong mixing
• Random cluster dynamics for the Ising model is rapidly mixing
• The effect of boundary conditions on mixing of 2D Potts models at discontinuous phase transitions
• Bound on the mass gap for finite volume stochastic Ising models at low temperature
• Mixing properties and exponential decay for lattice systems in finite volumes.
• On the two-dimensional dynamical Ising model in the phase coexistence region
• Quasi-polynomial mixing of the 2D stochastic Ising model with ``plus boundary up to criticality
• Exact thresholds for Ising-Gibbs samplers on general graphs
• The Swendsen-Wang process does not always mix rapidly
• Random-cluster dynamics in \(\mathbb {Z}^2\)
• Tight bounds for mixing of the Swendsen-Wang algorithm at the Potts transition point
• Comparison of Swendsen-Wang and heat-bath dynamics
• Approximating the Permanent
• Improved Bounds for Mixing Rates of Markov Chains and Multicommodity Flow
• Exponentially slow mixing in the mean-field Swendsen-Wang dynamics
• Mixing Times of Critical Two‐Dimensional Potts Models
• Swendsen--Wang Is Faster than Single-Bond Dynamics
• Information percolation and cutoff for the random‐cluster model
• Dynamics for the mean-field random-cluster model
• Swendsen-Wang Algorithm on the Mean-Field Potts Model
• The Random-Cluster Model
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
• Quasi-factorization of the entropy and logarithmic Sobolev inequalities for Gibbs random fields

This page was built for publication: Random-cluster dynamics in \(\mathbb{Z}^2\): rapid mixing with general boundary conditions