The critical Ising lines of the d=2 Ashkin-Teller model

TL;DR

This paper uses the universal critical point ratio $Q$ to accurately locate the critical Ising transition lines in the phase diagram of the 2D Ashkin-Teller model, combining finite-size scaling and transfer-matrix data.

Contribution

It introduces a leading-order expansion of $Q$ in a thermal field and fits it to transfer-matrix data to determine critical lines.

Findings

Accurate determination of Ising transition lines in the Ashkin-Teller model.

Development of a finite-size scaling expansion for the ratio $Q$.

Successful fitting of theoretical expressions to transfer-matrix data.

Abstract

The universal critical point ratio $Q$ is exploited to determine positions of the critical Ising transition lines on the phase diagram of the Ashkin-Teller (AT) model on the square lattice. A leading-order expansion of the ratio $Q$ in the presence of a non-vanishing thermal field is found from finite-size scaling and the corresponding expression is fitted to the accurate perturbative transfer-matrix data calculations for the $L\times L$ square clusters with $L\leq 9$.