Numerical Results for the Ground-State Interface in a Random Medium

Details Numerical Results for the Ground-State Interface in a Random Medium Numerical Results for the Ground-State Interface in a Random Medium

1995-07-29

arxiv.org/abs/cond-mat/9507130v1

Physics

Condensed Matter

10 pages, REVTEX3.0; 3 ps files (separate:tar/gzip/uuencoded) for figures

Scientific paper

10.1103/PhysRevE.52.R3337

The problem of determining the ground state of a $d$-dimensional interface embedded in a $(d+1)$-dimensional random medium is treated numerically. Using a minimum-cut algorithm, the exact ground states can be found for a number of problems for which other numerical methods are inexact and slow. In particular, results are presented for the roughness exponents and ground-state energy fluctuations in a random bond Ising model. It is found that the roughness exponent $\zeta = 0.41 \pm 0.01, 0.22 \pm 0.01$, with the related energy exponent being $\theta = 0.84 \pm 0.03, 1.45 \pm 0.04$, in $d = 2, 3$, respectively. These results are compared with previous analytical and numerical estimates.

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