Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2000-04-16
Phys. Rev. E 62, 3230 (2000)
Physics
Condensed Matter
Disordered Systems and Neural Networks
Submitted to Phys. Rev. E
Scientific paper
10.1103/PhysRevE.62.3230
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.
Alava Mikko J.
Duxbury Philip M.
Seppala E. T.
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