# Multicanonical Study of Continuum Physics in the D=2 $O(3)$ Nonlinear Sigma Model

## TL;DR

This study uses a multicanonical ensemble approach to analyze the continuum physics of the D=2 O(3) nonlinear sigma model, confirming asymptotic freedom and accurately estimating the mass gap.

## Contribution

It introduces a multicanonical ensemble method to study twisted spin configurations and determines the mass gap, aligning numerical results with analytical predictions.

## Key findings

- Finite size scaling confirms asymptotic freedom.
- Mass gap estimate matches Bethe Ansatz result.
- Determined the shift in the stiffness correlation length.

## Abstract

Employing a variant of the Multicanonical Ensemble we study twisted spin configurations on periodic boxes in the $D=2$ $O(3)$ nonlinear sigma model for $\beta$-values inbetween $1.55$ to $3.1$. The free energy difference of twisted spin configurations is determined from the constraint effective potential. The finite size scaling behavior is in accordance with the asymptotically free nature of the continuum theory. Upon certain reasonable assumptions we determine the $\Delta \beta( \beta)$-shift of the stiffness correlation length $\xi_s$. The mass-gap as determined by our analysis is ${m_0}=79.6(1.9)~\Lambda_{latt}$. This value agrees with the analytical result of the thermodynamic Bethe Ansatz ${m_0}=80.1~\Lambda_{latt}$.