Power law decay at criticality for the q-state antiferromagnetic Potts model on regular trees

TL;DR

This paper proves that the magnetic moment in the q-state antiferromagnetic Potts model on regular trees decays according to a power law at criticality, with an exponent of 1/2, under certain conditions.

Contribution

It provides a rigorous proof of power law decay at criticality for the model and confirms the exact decay exponent, extending understanding of phase transitions in these systems.

Findings

Power law decay of magnetic moment at critical temperature.

Exact decay exponent is 1/2.

Proof relies on established uniqueness conditions.

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.