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：我们证明了反铁磁Potts模型在树结构上具有强空间混合性质，其参数范围接近最优。本研究对Chen、Liu、Mani与Moitra的最新成果[arXiv.2304.01954]形成补充，该成果在无限温度条件下（对应均匀真染色情形）证明了该性质。此外，我们证明了弱空间混合结果，进一步完善了[arXiv.2304.01954]中的结论。