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

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

2004-06-15

arxiv.org/abs/hep-lat/0406023v2

Nucl.Phys. B704 (2005) 527-551

Physics

High Energy Physics

High Energy Physics - Lattice

27 pages, 8 figures. v2: Improved presentation, updated references. Nucl. Phys. B in press

Scientific paper

10.1016/j.nuclphysb.2004.10.021

We determine the scaling equation of state of the three-dimensional O(N) universality class, for N=5, 6, 32, 64. 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 obtain the critical exponents and the small-field, high-temperature, expansion of the effective potential (Helmholtz free energy) by analyzing the available perturbative series, in both fixed-dimension and epsilon-expansion schemes. Then, we determine the critical equation of state by using a systematic approximation scheme, based on polynomial representations valid in the whole critical region, which satisfy the known analytical properties of the equation of state, take into account the Goldstone singularities at the coexistence curve and match the small-field, high-temperature, expansion of the effective potential. This allows us also to determine several 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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