Universal ratios along a line of critical points. The Ashkin--Teller model

TL;DR

This paper investigates the two-dimensional Ashkin-Teller model, analyzing its line of critical points through sine-Gordon field theory, and computes universal amplitude ratios using form factor methods.

Contribution

It provides the first calculation of universal amplitude ratios along a critical line in the Ashkin-Teller model using integrable quantum field theory techniques.

Findings

Universal amplitude ratios are computed along the critical line.

The sine-Gordon model effectively describes the scaling limit.

Results are obtained within the two-particle approximation.

Abstract

The two-dimensional Ashkin-Teller model provides the simplest example of a statistical system exhibiting a line of critical points along which the critical exponents vary continously. The scaling limit of both the paramagnetic and ferromagnetic phases separated by the critical line are described by the sine-Gordon quantum field theory in a given range of its dimensionless coupling. After computing the relevant matrix elements of the order and disorder operators in this integrable field theory, we determine the universal amplitude ratios along the critical line within the two-particle approximation in the form factor approach.