  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.
