GLASS PHASE OF 2-DIMENSIONAL TRIANGULAR ELASTIC LATTICES WITH DISORDER

We study two-dimensional triangular elastic lattices in a background o f point disorder, excluding dislocations (tethered network). Using bot h (replica symmetric) static and (equilibrium) dynamic renormalization group (RG) for the corresponding N=2 component model, we find a trans ition to a glass phase for T<T-g, described by a plane of perturbative fixed points. The growth of displacements is found to be asymptotical ly isotropic with u(T)(2) similar to u(L)(2) similar to A(1)In(2)r, wi th universal subdominant anistropy u(T)(2)-u(L)(2) similar to A(2)Inr, where A(1) and A(2) depend continuously on temperature and the Poisso n ratio sigma. We also obtain the continuously varying dynamical expon ent 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 pu blished results in the literature. We find that our result reconciles the order of magnitude of the RG predictions with the most recent nume rical simulations.