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

We study the effective potential of three-dimensional O(N) models. In stati stical physics the effective potential represents the free-energy density a s a function of the order parameter (Helmholtz free energy), and, therefore , it is related to the equation of state. In particular, we consider its sm all-field expansion in the symmetric (high-temperature) phase, whose coeffi cients are related to the zero-momentum 2j-point renormalized coupling cons tants g(2j). For generic values of N, we calculate g(2j) to three loops in the field-theoretic approach based on the E-expansion. The estimates of g(2 j), or equivalently of r(2j) = g(2j)/g(4)(j-1), are obtained by a constrain ed analysis of the series that takes into account the exact results in one and zero dimensions. (C) 2000 Elsevier Science B.V. All rights reserved.