The effect of boundary conditions on mixing of 2D Potts models at discontinuous phase transitions

DOI10.1214/18-EJP180zbMath1410.60092arXiv1701.00181OpenAlexW2570641763MaRDI QIDQ1663879

Eyal Lubetzky, Reza Gheissari

Publication date: 24 August 2018

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.00181

zbMATH Keywords

boundary conditionssurface tensionPotts modelmixing timesSwendsen-Wang

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) Critical phenomena in equilibrium statistical mechanics (82B27)

Related Items

Random-cluster dynamics in \(\mathbb{Z}^2\): rapid mixing with general boundary conditions, Double Flip Move for Ising Models with Mixed Boundary Conditions, Cutoff for the Swendsen-Wang dynamics on the lattice, Spatial mixing and the random‐cluster dynamics on lattices, Unnamed Item, Tunneling behavior of Ising and Potts models in the low-temperature regime, Local and global geometry of the 2D Ising interface in critical prewetting, Random-cluster dynamics on random regular graphs in tree uniqueness

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Can extra updates delay mixing?
• 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 \(q \geqslant 1\)
• Geometric bounds for eigenvalues of Markov chains
• Interfaces in the Potts model. I: Pirogov-Sinai theory of the Fortuin- Kasteleyn representation
• Interfaces in the Potts model. II: Antonov's rule and rigidity of the order disorder interface
• On the mixing time of the 2D stochastic Ising model with ``Plus boundary conditions at low temperature
• Comparison theorems for reversible Markov chains
• 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
• 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
• Mixing Times of Critical Two‐Dimensional Potts Models
• Rapid mixing of Swendsen–Wang dynamics in two dimensions