An investigation of the phase structure of the two-dimensional O(2) and O(4) symmetric nonlinear sigma-models

Abstract

We investigate the phase structure of the two-dimensional O(2) and O(4) lattice σ-models by means of a Monte Carlo simulation using Binder's phenomenological renormalization group. For the O(2) model the transition temperature βc−1 is estimated and the expected line of critical points is found. For the O(4) model no signal of a phase transition is found in the range of couplings considered. This is in contradiction to a recent claim that the O(4) model has a critical point at finite β.