Finite-size scaling of the helicity modulus of the two-dimensional O(3) model

TL;DR

This study uses Monte Carlo simulations to analyze the finite-size scaling of the helicity modulus in the 2D O(3) model, providing insights into the validity of low temperature expansions and the likelihood of a Kosterlitz-Thouless transition.

Contribution

It offers the first detailed comparison between Monte Carlo results and low temperature expansion predictions for the 2D O(3) model's helicity modulus.

Findings

Finite-size scaling function matches low temperature expansion at low T

Range of validity for low T expansion is estimated

Evidence suggests no Kosterlitz-Thouless transition at T > 0

Abstract

Using Monte Carlo methods, we compute the finite-size scaling function of the helicity modulus $\Upsilon$ of the two-dimensional O(3) model and compare it to the low temperature expansion prediction. From this, we estimate the range of validity for the leading terms of the low temperature expansion of the finite-size scaling function and for the low temperature expansion of the correlation length. Our results strongly suggest that a Kosterlitz-Thouless transition at a temperature $T > 0$ is extremely unlikely in this model.