Super-rough glassy phase of the random field XY model in two dimensions
A. Perret1, Z. Ristivojevic2, P. Le Doussal2, G. Schehr1, K.J. Wiese2
1Laboratoire de Physique Théorique et Modèles Statistiques, CNRS-Université Paris-Sud, Bát. 100, 91405 Orsay France.
2CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France.
Abstract
We study both analytically, using the Renormalization Group (RG) to two loop order, and numerically, using an exact polynomial algorithm, the disorder-induced glass phase of the two-dimensional XY model with quenched random symmetry-breaking fields and without vortices. In the super-rough glassy phase, i.e. below the critical temperature Tc, the disorder and thermally averaged correlation function B(r) of the phase field θ(x), B(r) = ⟨[θ (x) - θ (x + r)]2⟩ behaves, for r « a, as B(r) ≅ A(τ) log2(r/a) where r = |r|, and a is a microscopic length scale. We derive the RG equations up to cubic order in τ = (Tc - T)/Tc and predict the universal amplitude A(τ) = 2 τ2 - 2 τ3 + O (τ4). Using an exact polynomial algorithm on an equivalent dimer version of the model we compute A(τ) numerically and obtain a remarkable agreement with our analytical prediction, up to τ ≈ 0.5.
arXiv:1204.5685 [pdf]
Phys. Rev. Lett. 109 (2012) 157205 [pdf]
Copyright (C) by Kay Wiese. Last edited April 27, 2012.