We present a proof of the power law decay of magnetic moment for the $q$-state antiferromagnetic Potts model on the regular tree at the critical temperature, and also justify that the exact exponent is $\frac{1}{2}$. Our proof relies on the assumption of the uniqueness at the critical temperature, which has been established for $q=3,4$, and for $q \ge 5$ with large degree. An iterative contraction inequality is developed for independent interests.

翻译：我们提出一个证据,证明在临界温度下,正树上正方形树上的 $q$-state efferrogatetic Pototts 模型磁时的电法衰减,并且证明准确的指数是$\frac{1\ ⁇ 2}$。 我们的证据依据的假设是关键温度的独特性,确定临界温度为$q=3,4美元,大程度上为$q\ge 5美元。一种迭接的收缩不平等是为独立利益而形成的。