2004/09/13 by Agostino Butti, Francesco Parisen Toldin, Andrea Pelissetto +1
Physics and Astronomy · #hep-lat
paper · pdf · doi:10.1016/j.nuclphysbps.2004.11.369
published as Nucl. Phys. B Proc. Suppl. 140 (2005), 808-810 · 3 pages, 2 figures. Talk presented at Lattice2004(spin), Fermilab, June 21-26, 2004
arxiv created 2004/09/13 · arxiv updated 2009/12/01
We determine the critical equation of state of the three-dimensional O(N) universality class, for N=4, 5, 6, 32, 64. The N=4 is relevant for the chiral phase transition in QCD with two flavors, the N=5 model is relevant for the SO(5) theory of high-Tc superconductivity, while the N=6 model is relevant for the chiral phase transition in two-color QCD with two flavors. We first consider the small-field expansion of the effective potential (Helmholtz free energy). Then, we apply a systematic approximation scheme based on polynomial parametric representations that are valid in the whole critical regime, satisfy the correct analytic properties (Griffiths' analyticity), take into account the Goldstone singularities at the coexistence curve, and match the small-field expansion of the effective potential. From the approximate representations of the equation of state, we obtain estimates of universal amplitude ratios. We also compare our approximate solutions with those obtained in the large-N expansion, up to order 1/N, finding good agreement for N \gtrsim 32.