Behavior near $θ=π$ of the mass gap in the 2D O(3) non-linear sigma model

Abstract

The validity of the Haldane's conjecture entails that the mass gap of the 2-dimensional O(3) non-linear sigma model with a $θ$-term must tend to zero as $θ$ approaches the value $π$ by following a precise law. In the present paper we extract the related critical exponents by simulating the model at imaginary $θ$.

24 pages, LaTeX source and 5 eps figures