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

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].

24 pages; We have made several small modifications based on suggestions by two anonymous referees. In particular a small error in the statement of Thm 3 has been corrected. No significant changes