The finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model

TL;DR

This paper develops nonlinear integral equations to describe the complete finite size energy spectrum of the 2D O(3) nonlinear sigma-model, validating results against known theories across different volume scales.

Contribution

It introduces a novel set of nonlinear integral equations for the finite size spectrum of the O(3) sigma-model, bridging small and large volume regimes.

Findings

Numerical energy spectra match rotator and perturbative predictions at small volumes.

Results agree with generalized Luscher formulas at large volumes.

Provides a comprehensive framework for finite size effects in the model.

Abstract

Nonlinear integral equations are proposed for the description of the full finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model in a periodic box. Numerical results for the energy eigenvalues are compared to the rotator spectrum and perturbation theory for small volumes and with the recently proposed generalized Luscher formulas at large volumes.