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.
Categories: math.PR cs.DM math-ph math.CO math.MP