Nonlinear $\sigma$-model, form factors and universality

TL;DR

This study uses high-statistics Monte Carlo simulations to investigate the continuum limit of the 2D O(3) non-linear sigma model, revealing discrepancies with form factor predictions and confirming universality with the dodecahedron model.

Contribution

It provides the first high-precision Monte Carlo analysis of the continuum limit of the 2D O(3) sigma model and compares it with theoretical form factor predictions.

Findings

Discrepancy between Monte Carlo data and form factor predictions.

Confirmation of universality between O(3) and dodecahedron models.

High-statistics data improves understanding of the continuum limit.

Abstract

We report the results of a very high statistics Monte Carlo study of the continuum limit of the two dimensional O(3) non-linear $\sigma$ model. We find a significant discrepancy between the continuum extrapolation of our data and the form factor prediction of Balog and Niedermaier, inspired by the Zamolodchikovs' S-matrix ansatz. On the other hand our results for the O(3) and the dodecahedron model are consistent with our earlier finding that the two models possess the same continuum limit.