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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Bencs, F., Berrekkal, K., & Regts, G. (2023). Near optimal bounds for weak and strong spatial mixing for the anti-ferromagnetic Potts model on trees. doi:10.48550/arXiv.2310.04338