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

Abstract

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.

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

References in corpus (1)

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