The effective potential of N-vector models: a field-theoretic study to O(ε^3)

Details The effective potential of N-vector models: a field-theoretic study to O(ε^3) The effective potential of N-vector models: a field-theoretic study to O(ε^3)

1999-11-28

arxiv.org/abs/cond-mat/9911452v2

Nucl.Phys. B575 (2000) 579-598

Physics

Condensed Matter

Statistical Mechanics

22 pages, RevTex, Nucl. Phys. B, in press

Scientific paper

10.1016/S0550-3213(00)00085-7

We study the effective potential of three-dimensional O($N$) models. In statistical physics the effective potential represents the free-energy density as a function of the order parameter (Helmholtz free energy), and, therefore, it is related to the equation of state. In particular, we consider its small-field expansion in the symmetric (high-temperature) phase, whose coefficients are related to the zero-momentum $2j$-point renormalized coupling constants $g_{2j}$. For generic values of $N$, we calculate $g_{2j}$ to three loops in the field-theoretic approach based on the $\epsilon$-expansion. The estimates of $g_{2j}$, or equivalently of $r_{2j}\equiv g_{2j}/g_4^{j-1}$, are obtained by a constrained analysis of the series that takes into account the exact results in one and zero dimensions.

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