Equation of State for Spin Systems with Goldstone Bosons: the 3d O(4) Case

Abstract

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.

20 pages, 3 figures

References in corpus (5)

• Correlation lengths and scaling functions in the three-dimensional O(4) model
• The 3-D O(4) universality class and the phase transition in two-flavor QCD
• The deconfining phase transition in full QCD with two dynamical flavors
• Critical behaviour and scaling functions of the three-dimensional O(6) model
• What is the order of the deconfining phase transition?

Cited by in corpus (5)

• The scaling functions of the free energy density and its derivatives for the 3d O(4) model
• Scaling functions for the O(4)-model in d=3 dimensions
• Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}({\partial }^4)$
• Finite size dependence of scaling functions of the three-dimensional O(4) model in an external field
• Universality and Scaling at the chiral transition in two-flavor QCD at finite temperature