Glass phase of two-dimensional triangular elastic lattices with disorder

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 (RG) 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) similar to u(L)(2) similar to A(1)In(2)r, with 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 Poisson ratio sigma. 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 literature. We find that our result reconciles the order of magnitude of the RG predictions with the most recent numerical simulations.