  We propose an improved parametric form for the equation of state of
three-dimensional O(N) spin systems. The proposed form is a series expansion
with two sets of terms, which contribute (mainly) separately to the description
of the high- and low-temperature regions of the phase diagram. Our goal is a
better description of the low-temperature phase at zero magnetic field (i.e.
the coexistence line), characterized by singularities induced by Goldstone
modes. We test our proposed form by comparison with existing Monte Carlo data
for the N=4 case, which is of interest in studies of the QCD phase transition
and for which the Goldstone-mode effects are quite pronounced. We find that the
description of the numerical equation of state is indeed improved with respect
to other fitting forms. In all cases considered we determine the coefficients
nonperturbatively, from fits to the data. As a consequence, we are able to
obtain a very precise characterization of the pseudo-critical line for the
model.
