Nonlinear $σ$-model, form factors and universality

We report the results of a very high statistics Monte Carlo study of the continuum limit of the two dimensional O(3) non-linear $σ$ 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.

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