Comparison of the O(3) bootstrap a model with lattice regularization at low energies

The renormalized coupling g(R) defined through the connected four-point function at zero external momentum in the nonlinear O(3) sigma model in two dimensions is computed in the continuum form factor bootstrap approach with an estimated error similar to 0.3%. New high precision data are presented for g(R) in the lattice-regularized theory with the standard action for nearly thermodynamic lattices L/xi similar to 7 and correlation lengths xi up to similar to 122 and with the fixed point action for correlation lengths up to similar to 12. The agreement between the form factor and lattice results is within similar to 1%. We also recompute the phase shifts at low energy by measuring two-particle energies at finite volume, a task which was previously performed by Luscher and Wolff using the standard action, but this time using the fixed point action. Excellent agreement with the Zamolodchikov S matrix is found. [S0556-2821(99)04419-7].