  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 in the following. As a
by-product we calculate critical exponents and amplitudes and confirm our
former results.
