SCALING FUNCTIONS AND EQUATIONS OF STATE FOR NONLINEAR SIGMA-MODELS

A simple method is presented which allows for a systematic extrapolati on and resummation of the loop expansion for nonlinear sigma-models. T he result guarantees renormalizability, the correct critical exponents to the order the loop expansion was carried out exactly, and a physic al solution in the high-temperature phase. As applications we use rece nt four-loop results to calculate the equation of state for the Heisen berg ferromagnet, and the scaling function for the Anderson transition , both with and without time-reversal invariance.