Nonlinear Sigma Model: Three Loops Renormalization and Lattice Scaling

摘要

The first nonuniversal terms of the renormalization group functions for the nonlinear sigma-model regularized on a lattice, for a choice of different lattice actions were calculated. Such terms fix the leading corrections to universal asymptotic scaling. However, comparison with Monte Carlo simulations shows that the actual deviations from universal scaling are due to nonperturbative effects, and not to perturbative analytic corrections. The latter are nonetheless relevant to determine the ratios of scaling operators to lambda-parameters.