No abstract

No abstract

No abstract

No abstract

In dimension D ≤ 2 the low temperature behavior of systems enjoying a continuous symmetry is dominated by super-instantons: classical configurations of arbitrarily low energy. Perturbation theory in the background of a super-instanton produces thermodynamic answers for the invariant Green's functions that differ from the standard ones, but only in non-Abelian models and only starting at O(1/β 2 ). This effect modifies the β-function of the O(N ) models and persists in the large N limit of the O(N ) models.

No abstract

The renormalized coupling g R defined through the connected four-point function at zero external momentum in the nonlinear O͑3͒ sigma model in two dimensions is computed in the continuum form factor bootstrap approach with an estimated error ϳ0.3%. New high precision data are presented for g R in the latticeregularized theory with the standard action for nearly thermodynamic lattices L/ϳ7 and correlation lengths up to ϳ122 and with the fixed point action for correlation lengths up to ϳ12. The agreement between the form factor and lattice results is within ϳ1%. We also recompute the phase shifts at low energy by measuring two-particle energies at finite volume, a task which was previously performed by Lüscher and Wolff using the standard action, but this time using the fixed point action. Excellent agreement with the Zamolodchikov S matrix is found. ͓S0556-2821͑99͒04419-7͔

The intrinsic 4-point coupling, defined in terms of a truncated 4-point function at zero momentum, provides a well-established measure for the interaction strength of a QFT. We show that this coupling can be computed nonperturbatively and to high accuracy from the form factors of an (integrable) QFT. The technique is illustrated and tested with the Ising model, the XYmodel and the O(3) nonlinear sigma-model. The results are compared to those from high precision lattice simulations.