O(3) model with Nienhuis action

TL;DR

This paper investigates a simplified lattice formulation of the O(3) sigma model using a Nienhuis action, demonstrating that it retains the correct continuum limit and enabling more efficient Monte Carlo simulations.

Contribution

It introduces a linearized Boltzmann weight formulation of the O(3) model that remains positive in the loop representation, facilitating improved simulation methods.

Findings

The loop model remains positive despite the sign problem in the spin formulation.

The simplified action reproduces the correct universal continuum limit.

Monte Carlo simulations confirm the mass gap scaling behavior.

Abstract

We study the O(3) sigma model in $D=2$ on the lattice with a Boltzmann weight linearized in $\beta$ on each link. While the spin formulation now suffers from a sign-problem the equivalent loop model remains positive and becomes particularly simple. By studying the transfer matrix and by performing Monte Carlo simulations in the loop form we study the mass gap coupling in a step scaling analysis. The question addressed is, whether or not such a simplified action still has the right universal continuum limit. If the answer is affirmative this would be helpful in widening the applicability of worm algorithm methods.