External field dependence of the correlation lengths in the three-dimensional O(4) model

TL;DR

This study numerically examines how external magnetic fields influence the transverse and longitudinal correlation lengths in the 3D O(4) model, confirming theoretical predictions and deriving universal scaling functions.

Contribution

It provides the first detailed numerical verification of the H^{-1/2} dependence of the transverse correlation length and derives the universal scaling function for the model.

Findings

Confirmed the H^{-1/2} dependence of the transverse correlation length in the low-temperature phase.

Found the universal amplitude ratio xi^c_T / xi^c_L = 1.99(1) on the critical line.

Derived the universal scaling function for the transverse correlation length.

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. In the low-temperature phase we verify explicitly the H^{-1/2}-dependence of the transverse correlation length, which is expected due to the Goldstone modes of the model. On the critical line we find the universal amplitude ratio xi^c_T / xi^c_L = 1.99(1). From our data we derive the universal scaling function for the transverse correlation length. The H-dependencies of the correlation lengths in the high temperature phase are discussed and shown to be in accord with the scaling functions.