2021/12/01 by Gu, Chenlin, Wu, Wei, Yang, Kuan
#05C99 #60K35 #82B20 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
paper · doi:10.48550/arxiv.2112.00573
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 (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 ≥ 5 with large degree. An iterative contraction inequality is developed for independent interests.