Critical behaviour of the O(3) nonlinear sigma model with topological term at theta=pi from numerical simulations

TL;DR

This study uses numerical simulations to analyze the critical behavior of the 2D O(3) nonlinear sigma model with a topological term at theta=pi, suggesting a second order phase transition consistent with a specific conformal field theory.

Contribution

It introduces a method combining simulations at imaginary theta and scaling transformations to explore the model's critical behavior at real theta values.

Findings

Evidence of a second order phase transition at theta=pi

Critical exponents match SU(2)_1 Wess-Zumino-Novikov-Witten model

Results valid for small coupling values

Abstract

We investigate the critical behaviour at theta=pi of the two-dimensional O(3) nonlinear sigma model with topological term on the lattice. Our method is based on numerical simulations at imaginary values of theta, and on scaling transformations that allow a controlled analytic continuation to real values of theta. Our results are compatible with a second order phase transition, with the critical exponent of the SU(2)_1 Wess-Zumino-Novikov-Witten model, for sufficiently small values of the coupling.