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Multi-particle form factors of local operators in integrable models in two dimensions seem to have the property that they factorize when one subset of the particles in the external states are boosted by a large rapidity with respect to the others. This remarkable property, which goes under the name of form factor clustering, was first observed by Smirnov in the O(3) non-linear sigma-model and has subsequently found useful applications in integrable models without internal symmetry structure. In this paper we conjecture the nature of form factor clustering for the general O(n) sigma-model and make some tests in leading orders of the 1/n expansion and for the special cases n=3,4.
TBA integral equations are proposed for 1-particle states in the sausage- and SS-models and their $sigma$-model limits. Combined with the ground state TBA equations the exact mass gap is computed in the O(3) and O(4) nonlinear $sigma$-model and the r
We analyze the free energy of the integrable two dimensional O(4) sigma model in a magnetic field. We use Volins method to extract high number (2000) of perturbative coefficients with very high precision. The factorial growth of these coefficients ar
A non-perturbative Renormalization Group approach is used to calculate scaling functions for an O(4) model in d=3 dimensions in the presence of an external symmetry-breaking field. These scaling functions are important for the analysis of critical be
Recently it was shown that the scaling dimension of the operator $phi^n$ in $lambda(phi^*phi)^2$ theory may be computed semi-classically at the Wilson-Fisher fixed point in $d=4-epsilon$, for generic values of $lambda n$ and this was verified to two
We study dual strong coupling description of integrability-preserving deformation of the $O(N)$ sigma model. Dual theory is described by a coupled theory of Dirac fermions with four-fermion interaction and bosonic fields with exponential interactions