Critical Behavior for 2d Uniform and Disordered Ferromagnets at Self-Dual Points

TL;DR

This paper investigates critical phenomena at self-dual points in 2D uniform and disordered ferromagnets, showing that these points exhibit hallmark features of phase transitions such as infinite susceptibility and power-law decay of correlations.

Contribution

It establishes that self-dual points in certain 2D systems, including disordered models, display critical behavior with specific properties like infinite susceptibility.

Findings

Self-dual points exhibit critical behavior in 2D systems.

Disordered models at self-dual points show power-law decay of correlations.

Infinite susceptibility and vanishing magnetization are observed at these points.

Abstract

We consider certain two-dimensional systems with self--dual points including uniform and disordered $q$-state Potts models. For systems with continuous energy density (such as the disordered versions) it is established that the self--dual point exhibits critical behavior: Infinite susceptibility, vanishing magnetization and power law bounds for the decay of correlations.