Periodic elastic medium in which periodicity is relevant,

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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 Ld−1×λ and these coupling constants are periodically repeated, with a period λ, 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∼L2/3,L≪Lc and w∼L1/2,L≫Lc with Lc∼λ3/2 in (1+1) dimensions, and w∼L0.42,L≪Lc and w∼ln(L),L≫Lc with Lc∼λ2.38 in (2+1) dimensions.

Details

Original languageEnglish
Pages (from-to)3230-3233
JournalPhysical Review E
Volume62
Issue number3
Publication statusPublished - 2000
MoE publication typeA1 Journal article-refereed

ID: 3412152