# Transition temperature scaling in weakly coupled two-dimensional Ising models

## TL;DR

This paper studies how the transition temperature in weakly coupled 2D Ising models scales with susceptibility, revealing the need for a logarithmic correction due to the heat capacity exponent approaching zero.

## Contribution

It provides a precise analysis of the transition temperature scaling and highlights the role of topological excitations and logarithmic corrections in weakly coupled 2D Ising models.

## Key findings

- Transition temperature scales with susceptibility exponent γ.
- An additional logarithmic factor is necessary for accurate prediction.
- Topological excitations significantly influence the model's behavior.

## Abstract

We investigate the proposal that for weakly coupled two-dimensional magnets the transition temperature scales with a critical exponent which is equivalent to that of the susceptibility in the underlying two-dimensional model, $ \gamma $. Employing the exact diagonalization of transfer matrices we can determine the critical temperature for Ising models accurately and then fit to approximate this critical exponent. We find an additional logarithm is required to predict the transition temperature, stemming from the fact that the heat capacity exponent $ \alpha $ tends to zero for this Ising model, complicating the elementary prediction. We believe that the excitations of the transfer matrix correspond to thermalized topological excitations of the model and find that even the simplest model exhibits significant changes of behavior for the most relevant of these excitations as the temperature is varied.