  Three-dimensional N-vector spin models may define universality classes for
such diverse phenomena as i) the superfluid transition in liquid helium
(currently investigated in the micro-gravity environment of the Space Shuttle)
and ii) the transition from hadronic matter to a quark-gluon plasma, studied in
heavy-ion collisions at the laboratories of Brookhaven and CERN. The models
have been extensively studied both by field-theoretical and by statistical
mechanical methods, including Monte Carlo simulations using cluster algorithms.
These algorithms are applicable also in the presence of a magnetic field. Key
quantities for the description of the transitions above -- such as universal
critical amplitude ratios and the location of the so-called pseudo-critical
line -- can be obtained from the models' magnetic equation of state, which
relates magnetization, external magnetic field and temperature. Here we present
an improved parametrization for the equation of state of the models, allowing a
better fit to the numerical data. Our proposed form is inspired by perturbation
theory, with coefficients determined nonperturbatively from fits to the data.
