Disordered XY Models and Coulomb Gases: Renormalization via Traveling Waves

David Carpentier and Pierre Le Doussal
Phys. Rev. Lett. 81, 2558 – Published 21 September 1998
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Abstract

We present a novel renormalization approach to 2D random XY models using direct and replicated Coulomb gas (CG) methods. By including fusion of environments (charge fusion in the replicated CG), the distribution of local disorder is found to obey a Kolmogorov nonlinear 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 random energy models. Finding marginal operators at the disorder-induced transition is related to the front velocity selection problem in KPP equations that yield new critical behavior. The method is applied to critical random Dirac problems.

  • Received 9 February 1998

DOI:https://doi.org/10.1103/PhysRevLett.81.2558

©1998 American Physical Society

Authors & Affiliations

David Carpentier and Pierre Le Doussal*

  • CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 Rue Lhomond, 75231 Paris, France

  • *Laboratoire propre associé à l'ENS et à Univ. Paris-Sud.

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Vol. 81, Iss. 12 — 21 September 1998

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