A periodic elastic medium in which periodicity is relevant

Abstract

We analyze, in both (1+1)- and (2+1)- dimensions, a periodic elastic medium in which the periodicity is such that at long distances the behavior is always in the random-substrate universality class. This contrasts with the models with an additive periodic potential in which, according to the field theoretic analysis of Bouchaud and Georges and more recently of Emig and Nattermann, the random manifold class dominates at long distances in (1+1)- and (2+1)-dimensions. The models we use are random-bond Ising interfaces in hypercubic lattices. The exchange constants are random in a slab of size $L^{d-1}\times \lambda$ and these coupling constants are periodically repeated along either {10} or {11} (in (1+1)-dimensions) and {100} or {111} (in (2+1)-dimensions). Exact ground-state calculations confirm scaling arguments which predict that the surface roughness $w$ behaves as: $w\sim L^{2/3},L\ll L_c$ and $w\sim L^{1/2},L\gg L_c$, with $L_c\sim {\lambda }^{3/2}$ in $(1+1)$-dimensions and; $w\sim L^{0.42},L\ll L_c$ and $w\sim \ln (L),L\gg L_c$, with $L_c\sim {\lambda }^{2.38}$ in $(2+1)$-dimensions.

Submitted to Phys. Rev. E

References in corpus (6)

• Absence of Two-Dimensional Bragg Glasses
• Quasi-static cracks and minimal energy surfaces
• Disorder Driven Roughening Transitions of Elastic Manifolds and Periodic Elastic Media
• Statistical Topography of Glassy Interfaces
• Roughening Transition of Interfaces in Disordered Systems
• Dislocations in the ground state of the solid-on-solid model on a disordered substrate

Cited by in corpus (2)

• Disorder Driven Critical Behavior of Periodic Elastic Media in a Crystal Potential
• Intermittence and roughening of periodic elastic media