Crossover functions by renormalization-group matching: Three-loop results

Abstract

Crossover functions are obtained to three-loop order in an expansion around dimension d=4 for the ${\phi }^4$ theory. Expressions for the internal energy, susceptibility, and correlation length are given for the general n-component system in zero magnetic field and above the critical temperature. The full Helmholtz free energy, magnetization equation of state, and susceptibility are given for the Ising-like n=1 case. Corrected values for the critical amplitude ratios as well as for the correction-to-scaling amplitude ratios are given to three-loop order.