Correlation lengths and scaling functions in the three-dimensional O(4) model

TL;DR

This paper numerically studies the correlation lengths and scaling functions in the 3D O(4) model, confirming critical behaviors, Goldstone effects, and universal amplitude ratios, and explores relations between correlation functions.

Contribution

It provides the first detailed numerical calculation of the scaling functions for both transverse and longitudinal correlation lengths in the 3D O(4) model, including Goldstone effects and universal ratios.

Findings

Scaling functions describe critical behavior and Goldstone effects.

Critical exponent delta=4.824(9) determined.

Universal amplitude ratios are calculated and validated.

Abstract

We investigate numerically the transverse and longitudinal correlation lengths of the three-dimensional O(4) model as a function of the external field H. From our data we calculate the scaling function of the transverse correlation length, and that of the longitudinal correlation length for T>T_c. We show that the scaling functions do not only describe the critical behaviours of the correlation lengths but encompass as well the predicted Goldstone effects, in particular the H^{-1/2}-dependence of the transverse correlation length for T<T_c. In addition, we determine the critical exponent delta=4.824(9) and several critical amplitudes from which we derive the universal amplitude ratios R_{chi}=1.084(18), Q_c=0.431(9), Q_2^T=4.91(8), Q_2^L=1.265(24) and U_{xi}^c=1.99(1). The last result supports a relation between the longitudinal and transverse correlation functions, which was conjectured to hold below T_c but seems to be valid also at T_c.