Glass phase of two-dimensional triangular elastic lattices with disorder

David Carpentier; Pierre Le Doussal

doi:10.1103/PhysRevB.55.12128

paper

Glass phase of two-dimensional triangular elastic lattices with disorder

arXiv:cond-mat/9611168 · doi:10.1103/PhysRevB.55.12128

Abstract

We study two dimensional triangular elastic lattices in a background of point disorder, excluding dislocations (tethered network). Using both (replica symmetric) static and (equilibrium) dynamic renormalization group for the corresponding $N = 2$ component model, we find a transition to a glass phase for $T < T_{g}$ , described by a plane of perturbative fixed points. The growth of displacements is found to be asymptotically isotropic with $u_{T}^{2} \sim u_{L}^{2} \sim A_{1} ln^{2} r$ , with universal subdominant anisotropy $u_{T}^{2} - u_{L}^{2} \sim A_{2} ln r$ . where $A_{1}$ and $A_{2}$ depend continuously on temperature and the Poisson ratio $σ$ . We also obtain the continuously varying dynamical exponent $z$ . For the Cardy-Ostlund $N = 1$ model, a particular case of the above model, we point out a discrepancy in the value of $A_{1}$ with other published results in the litterature. We find that our result reconciles the order of magnitude of the RG predictions with the most recent numerical simulations.

25 pages, RevTeX, uses epsf,multicol and amssymb

Glass phase of two-dimensional triangular elastic lattices with disorder

Abstract

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