Glass phase of two-dimensional triangular elastic lattices with disorder

Details Glass phase of two-dimensional triangular elastic lattices with disorder Glass phase of two-dimensional triangular elastic lattices with disorder

1996-11-21

arxiv.org/abs/cond-mat/9611168v1

Phys.Rev.B 55 (1997), p.12128

Physics

Condensed Matter

Disordered Systems and Neural Networks

25 pages, RevTeX, uses epsf,multicol and amssymb

Scientific paper

10.1103/PhysRevB.55.12128

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 $\sigma$. 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 litterature. We find that our result reconciles the order of magnitude of the RG predictions with the most recent numerical simulations.

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