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].

翻译：我们证明了树状反铁磁Potts模型在近最优参数范围内表现出强空间混合性。本研究补充了Chen、Liu、Mani和Moitra [arXiv.2304.01954] 的最新结果，该结果在无限温度设定（对应于均匀正常染色）中证实了这一现象。此外，我们还证明了弱空间混合性结论，作为对 [arXiv.2304.01954] 中结果的补充。