Disordered XY models and Coulomb gases: renormalization via traveling waves

Abstract

We present a novel RG approach to 2D random XY models using direct and replicated Coulomb gas methods. By including fusion of environments (charge fusion in the replicated CG) it follows the distribution of local disorder, found to obey a Kolmogorov non linear equation (KPP) with traveling wave solutions. At low T and weak disorder it yields a glassy XY phase with broad distributions and precise connections to Derrida's GREM. Finding marginal operators at the disorder-induced transition is related to the front velocity selection problem in KPP equations yielding new critical behaviour. The method is applied to critical random Dirac problems.