Longitudinal and transverse spectral functions in the three-dimensional [formula omitted] model

Abstract

We have performed a high statistics simulation of the O ( 4 ) model on a three-dimensional lattice of linear extension L = 120 for small external fields H. Using the maximum entropy method we analyze the longitudinal and transverse plane spin correlation functions for T < T c and T ⩾ T c . In the transverse case we find for all T and H a single sharp peak in the spectral function, whose position defines the transverse mass m T , the correlator is that of a free particle with mass m T . In the longitudinal case we find in the very high temperature region also a single sharp peak in the spectrum. On approaching the critical point from above the peak broadens somewhat and at T c its position m L is at 2 m T for all our H-values. Below T c we find still a significant peak at ω = 2 m T and at higher ω-values a continuum of states with several smaller peaks with decreasing heights. This finding is in accord with a relation of Patashinskii and Pokrovskii between the longitudinal and the transverse correlation functions. We test this relation and its range of applicability in the following. As a by-product we calculate critical exponents and amplitudes and confirm our former results.