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Power law decay at criticality for the q-state antiferromagnetic Potts model on regular trees (2112.00573v3)
Published 1 Dec 2021 in math.PR, cs.DM, math-ph, math.CO, and math.MP
Abstract: 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.