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

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