Uniqueness of the Gibbs measure for the 4-state anti-ferromagnetic Potts model on the regular tree

11/11/2020
by   David de Boer, et al.
0

We show that the 4-state anti-ferromagnetic Potts model with interaction parameter w∈(0,1) on the infinite (d+1)-regular tree has a unique Gibbs measure if w≥ 1-4/d+1 for all d≥ 4. This is tight since it is known that there are multiple Gibbs measures when 0≤ w<1-4/d+1 and d≥ 4. We moreover give a new proof of the uniqueness of the Gibbs measure for the 3-state Potts model on the (d+1)-regular tree for w≥ 1-3/d+1 when d≥ 3 and for w∈ (0,1) when d=2.

READ FULL TEXT
research
03/29/2022

Uniqueness of the Gibbs measure for the anti-ferromagnetic Potts model on the infinite Δ-regular tree for large Δ

In this paper we prove that for any integer q≥ 5, the anti-ferromagnetic...
research
04/10/2018

Uniqueness for the 3-State Antiferromagnetic Potts Model on the Tree

The antiferromagnetic q-state Potts model is perhaps the most canonical ...
research
12/12/2012

Loopy Belief Propogation and Gibbs Measures

We address the question of convergence in the loopy belief propagation (...
research
07/14/2020

On sampling symmetric Gibbs distributions on sparse random graphs and hypergraphs

We consider efficient algorithms for approximate sampling from symmetric...
research
12/01/2021

Uniqueness for the q-state antiferromagnetic Potts model on the regular tree

We present an elementary proof for the uniqueness regime of the general ...
research
03/15/2022

Optimal mixing for two-state anti-ferromagnetic spin systems

We prove an optimal Ω(n^-1) lower bound for modified log-Sobolev (MLS) c...
research
07/19/2021

Algorithms for general hard-constraint point processes via discretization

We study a general model for continuous spin systems with hard-core inte...

Please sign up or login with your details

Forgot password? Click here to reset