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

TL;DR

This paper investigates how the mass gap in the 2D O(3) non-linear sigma model behaves near θ=π, using simulations at imaginary θ to determine critical exponents and test Haldane's conjecture.

Contribution

It introduces a novel simulation approach at imaginary θ to analyze the mass gap behavior near θ=π in the 2D O(3) model.

Findings

Critical exponents for the mass gap near θ=π are extracted.

Results support the hypothesis that the mass gap tends to zero as θ approaches π.

The study validates the use of imaginary θ simulations for critical behavior analysis.

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 $\theta$-term must tend to zero as $\theta$ approaches the value $\pi$ by following a precise law. In the present paper we extract the related critical exponents by simulating the model at imaginary $\theta$.