Equations of state and renormalization-group recursion relations

Abstract

Renormalization-group recursion relations are used to construct equations of state to first order in $\epsilon =4-d$ for continuous spin models of critical behavior. The recursion relations map Hamiltonians out of the critical regime into regions of small correlation length, where Landau theory with fluctuation corrections is employed. This technique is used to discuss critical behavior along a $\lambda$ line of critical points, together with the effect of imposing an ordering field. An application of the method to tricritical phenomena is described briefly.