Numerical results for the ground-state interface in a random medium

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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 ζ=0.41±0.01,0.22±0.01, with the related energy exponent being θ=0.84±0.03,1.45±0.04, in d=2,3, respectively. These results are compared with previous analytical and numerical estimates.

Original languageEnglish (US)
Pages (from-to)R3337-R3340
JournalPhysical Review E
Volume52
Issue number4
DOIs
StatePublished - 1995

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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