Topological transitions and freezing in XY models and Coulomb gases with quenched disorder: renormalization via traveling waves

We study the two dimensional XY model with quenched random phases and its C oulomb gas formulation. A novel renormalization group (RG) method is develo ped which allows to study perturbatively the glassy low temperature XY phas e and the transition at which frozen topological defects (vortices) prolife rate. This RC approach is constructed both from the replicated Coulomb gas and, equivalently without the use of replicas, using the probability distri bution of the local disorder (random defect core energy). By taking into ac count the fusion of environments (i.e., charge fusion in the replicated Cou lomb gas) this distribution is shown to obey a Kolmogorov's type (KPP) non linear RG equation which admits traveling wave solutions and exhibits a fre ezing phenomenon analogous to glassy freezing in Derrida's random energy mo dels. The resulting physical picture is that the distribution of local diso rder becomes broad below a freezing temperature and that the transition is controlled by rare favorable regions for the defects, the density of which can be used as the new perturbative parameter. The determination of margina l directions at the disorder induced transition is shown to be related to t he well studied front velocity selection problem in the KPP equation and th e universality of the novel critical behaviour obtained here to the known u niversality of the corrections to the front velocity. Applications to other two dimensional problems are mentioned at the end. (C) 2000 Elsevier Scien ce B.V. All rights reserved.