Longitudinal and transverse spectral functions in the three-dimensional O(4) model

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 2m(T) for all our H-values. Below T-c we find still a significant peak at omega = 2m(T) and at higher omega-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. (C) 2010 Elsevier B.V. All rights reserved.