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

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

1999-08-24

arxiv.org/abs/cond-mat/9908335v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

86 pages, 15 eps files included

Scientific paper

10.1016/S0550-3213(00)00468-5

We study the two dimensional XY model with quenched random phases and its Coulomb gas formulation. A novel renormalization group (RG) method is developed which allows to study perturbatively the glassy low temperature XY phase and the transition at which frozen topological defects (vortices) proliferate. This RG approach is constructed both from the replicated Coulomb gas and, equivalently without the use of replicas, using the probability distribution of the local disorder (random defect core energy). By taking into account the fusion of environments (i.e charge fusion in the replicated Coulomb gas) this distribution is shown to obey a Kolmogorov's type (KPP) non linear RG equation which admits travelling wave solutions and exhibits a freezing phenomenon analogous to glassy freezing in Derrida's random energy models. The resulting physical picture is that the distribution of local disorder 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 marginal directions at the disorder induced transition is shown to be related to the well studied front velocity selection problem in the KPP equation and the universality of the novel critical behaviour obtained here to the known universality of the corrections to the front velocity. Applications to other two dimensional problems are mentionned at the end.

Affiliated with

Also associated with

No associations

Rating

Topological transitions and freezing in XY models and Coulomb gases with quenched disorder: renormalization via traveling waves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Topological transitions and freezing in XY models and Coulomb gases with quenched disorder: renormalization via traveling waves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Topological transitions and freezing in XY models and Coulomb gases with quenched disorder: renormalization via traveling waves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-677078