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

Abstract

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.

arXiv comment27 pages, 8 figures. v2: Improved presentation, updated references. Nucl. Phys. B in press

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• Instability of the O(5) multicritical behavior in the SO(5) theory of high-Tc superconductors
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• Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}({\partial }^4)$
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• Pseudo-$\epsilon$ Expansion and Renormalized Coupling Constants at Criticality
• Exact Lorentz-violating all-loop ultraviolet divergences in scalar field theories
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• Renormalization group approach for Lorentz-violating scalar field theory at all loop orders
• All-loop order critical exponents for massless scalar field theory with Lorentz violation in the BPHZ method
• Diffeomorphism symmetry effect on the O(N ) universality class
• Unconventional minimal subtraction and Callan-Symanzik methods for Lorentz-violating scalar field theories at all loop orders
• Universal effective couplings of the three-dimensional $n$-vector model and field theory
• Influence of conformal symmetry on the amplitude ratios for O($N$) models
• NLO critical exponents of O($N$) lambda ${\varphi }^4$ scalar field theories in curved spacetime