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

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.

Comments: 10 pages, 5 figures