Renormalization Group for Multiparticle Production in (2+1) Dimensions Around the Threshold

Multiparticle production in (2+1) dimensions is investigated. We show that in a small region around the threshold the perturbation theory becomes unapplicable due to infrared divergencies in a class of Feynman graphs with rescattering in final state. We develop a technique based on renormalization group for summing up leading logarithms and apply it to the $\phi^4$ models with and without symmetry breaking and to the $O(N)$ $\phi^4$ theory.