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We propose an improved parametric form for the equation of state ofthree-dimensional O(N) spin systems. The proposed form is a series expansionwith two sets of terms, which contribute (mainly) separately to the descriptionof the high- and low-temperature regions of the phase diagram. Our goal is abetter description of the low-temperature phase at zero magnetic field (i.e.the coexistence line), characterized by singularities induced by Goldstonemodes. We test our proposed form by comparison with existing Monte Carlo datafor the N=4 case, which is of interest in studies of the QCD phase transitionand for which the Goldstone-mode effects are quite pronounced. We find that thedescription of the numerical equation of state is indeed improved with respectto other fitting forms. In all cases considered we determine the coefficientsnonperturbatively, from fits to the data. As a consequence, we are able toobtain a very precise characterization of the pseudo-critical line for themodel.Comment: 20 pages, 3 figure

Equation of state for spin systems with Goldstone bosons: the 3d O(4) case