  We investigate numerically the three-dimensional O(4) model on 24^3-120^3
lattices as a function of the magnetic field H. We verify explicitly the
singularities induced by Goldstone modes in the low-temperature phase of the
model, and show that they are also observed close to the critical temperature.
Our results are well described by the perturbative form of the model's magnetic
equation of state, with coefficients determined nonperturbatively from our
data. The resulting expression is used to generate the magnetization's scaling
function parametrically.
