The effective potential of N-vector models: a field-theoretic study to O(ϵ3) Original Research Article

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 g2j. For generic values of N, we calculate g2j to three loops in the field-theoretic approach based on the ϵ-expansion. The estimates of g2j, or equivalently of r2j≡g2j/g4j−1, are obtained by a constrained analysis of the series that takes into account the exact results in one and zero dimensions.