We present an elementary proof for the uniqueness regime of the general $q$-state antiferromagnetic Potts model on the $d$-ary tree. The key observation is a positive association property of its boundary condition. We also obtain the exact exponential decay rate in all of the subcritical regime, and power law decay rate at the critical temperature.

翻译：我们提出一个基本证据,证明美元-国家通用反地磁器模型在美元-金树上的独特性。 关键观察是其边界状况的积极关联属性。 我们还获得了所有次临界系统中的精确指数衰减率,以及临界温度下的权力法衰减率。