Exponentially slow mixing in the mean-field Swendsen-Wang dynamics

DOI10.1214/18-AIHP955zbMath1434.60290OpenAlexW3004960718MaRDI QIDQ2179231

Eyal Lubetzky, Reza Gheissari, Yuval Peres

Publication date: 12 May 2020

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.aihp/1580720483

zbMATH Keywords

random graphsPotts modelmixing timeFK modelSwendsen-Wang

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) 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) Critical phenomena in equilibrium statistical mechanics (82B27)

Related Items

Entropy decay in the Swendsen-Wang dynamics on \(\mathbb{Z}^d\), Metastability in loss networks with dynamic alternative routing, Finite-size scaling, phase coexistence, and algorithms for the random cluster model on random graphs, Sampling from Potts on random graphs of unbounded degree via random-cluster dynamics, Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dynamic critical behavior of the Chayes-Machta algorithm for the random-cluster model. I: Two dimensions
• Glauber dynamics for the mean-field Potts model
• The random-cluster model on the complete graph
• Tight bounds for mixing of the Swendsen-Wang algorithm at the Potts transition point
• Mixing properties of the Swendsen–Wang process on the complete graph and narrow grids
• Comparison of Swendsen-Wang and heat-bath dynamics
• A power law of order 1/4 for critical mean-field Swendsen-Wang dynamics
• Random cluster dynamics for the Ising model is rapidly mixing
• Mixing Times of Critical Two‐Dimensional Potts Models
• Dynamics for the mean-field random-cluster model
• Swendsen-Wang Algorithm on the Mean-Field Potts Model
• The phase transition in the cluster‐scaled model of a random graph
• Time-Dependent Statistics of the Ising Model