Near optimal bounds for weak and strong spatial mixing for the anti-ferromagnetic Potts model on trees

2023/10/06 by Ferenc Bencs, Khallil Berrekkal, Bencs, Ferenc +3
Mathematics · #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2310.04338

openalex publication_date 2023/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the anti-ferromagnetic Potts model on trees exhibits strong spatial mixing for a near-optimal range of parameters. Our work complements recent results of Chen, Liu, Mani, and Moitra [arXiv.2304.01954] who showed this to be true in the infinite temperature setting, corresponding to uniform proper colorings. We furthermore prove weak spatial mixing results complementing results in [arXiv.2304.01954].

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