Locating analytically critical temperature in some statistical systems

TL;DR

This paper introduces a simple criterion for determining critical temperatures in statistical systems, successfully reproducing known results and proposing new conjectures for complex models.

Contribution

The authors present a novel, straightforward method to locate critical temperatures, extending its application to various models including non-selfdual systems and multi-layer configurations.

Findings

Accurately reproduces known critical temperatures for 2D Ising, Potts, and Z(N<5) models.

Predicts critical temperature for two coupled Ising layers as β_c=0.2656.

Relates 3D Ising critical temperature to the free energy of a two-layer system.

Abstract

We have found a simple criterion which allows for the straightforward determination of the order-disorder critical temperatures. The method reproduces exactly results known for the two dimensional Ising, Potts and $Z(N<5)$ models. It also works for the Ising model on the triangular lattice. For systems which are not selfdual our proposition remains an unproven conjecture. It predicts $\beta_c=0.2656...$ for the two coupled layers of Ising spins. Critical temperature of the three dimensional Ising model is related to the free energy of the two layer Ising system.