The scaling equation of state of the 3-D O(4) universality class

We determine the critical equation of state of the three-dimensional O(4)universality class. We first consider the small-field expansion of theeffective potential (Helmholtz free energy). Then, we apply a systematicapproximation scheme based on polynomial parametric representations that arevalid in the whole critical regime, satisfy the correct analytic properties(Griffiths' analyticity), take into account the Goldstone singularities at thecoexistence curve, and match the small-field expansion of the effectivepotential. From the approximate representations of the equation of state, weobtain estimates of several universal amplitude ratios. The three-dimensional O(4) universality class is expected to describe thefinite-temperature chiral transition of quantum chromodynamics with two lightflavors. Within this picture, the O(4) critical equation of state relates thereduced temperature, the quark masses, and the condensates around T_c in thelimit of vanishing quark masses.Comment: 19 pages, 5 fig