The super-rough phase of the Cardy-Ostlund model: two-loop results
Zoran Ristivojevic, Pierre Le Doussal, Kay Jörg Wiese
CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France.
Abstract
We consider the two-dimensional XY model with quenched random symmetry-breaking fields and excluded vortices. We study the vicinity of its glass transition temperature Tc, in an expansion in small τ = (Tc - T)/Tc where T denotes the temperature. We derive renormalization-group equations in cubic order in the anharmonicity, and show that they contain two universal invariants. Using them we obtain that the correlation function in the super-rough phase for temperature T < Tc behaves at large distances as ⟨[θ(x) - θ(0)]2⟩ = A ln2|x/a|+ O(ln|x/a|), where the amplitude A is a universal function of temperature A = 2 τ2 - 2 τ3 + O(τ4). This result differs at two-loop order, i.e. O(τ3), from the prediction based on results from the "nearly conformal" field theory of a related fermion model. We also obtain the correction-to-scaling exponent.
arXiv:1204.6221 [pdf]
Phys. Rev. B 86 (2012) 054201 [pdf]
Copyright (C) by Kay Wiese. Last edited April 27, 2012.