The scaling equation of state of the three-dimensional O(N) universality class: N >= 4

Details The scaling equation of state of the three-dimensional O(N) universality class: N >= 4 The scaling equation of state of the three-dimensional O(N) universality class: N >= 4

2004-09-13

arxiv.org/abs/hep-lat/0409054v1

Nucl. Phys. B Proc. Suppl. 140 (2005), 808-810

Physics

High Energy Physics

High Energy Physics - Lattice

3 pages, 2 figures. Talk presented at Lattice2004(spin), Fermilab, June 21-26, 2004

Scientific paper

10.1016/j.nuclphysbps.2004.11.36

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-T_c 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.

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