Correlation-length–exponent relation for the two-dimensional random Ising model

Péter Lajkó, Ferenc Iglói

Research output: Contribution to journalArticle

6 Citations (Scopus)


We consider the two-dimensional (2D) random Ising model on a diagonal strip of the square lattice, where the bonds take two values, [Formula Presented] with equal probability. Using an iterative method, based on a successive application of the star-triangle transformation, we have determined at the bulk critical temperature the correlation length along the strip [Formula Presented] for different widths of the strip [Formula Presented] The ratio of the two lengths [Formula Presented] is found to approach the universal value [Formula Presented] for large L, independent of the dilution parameter [Formula Presented] With our method we have demonstrated with high numerical precision, that the surface correlation function of the 2D dilute Ising model is self-averaging, in the critical point conformally covariant and the corresponding decay exponent is [Formula Presented]

Original languageEnglish
Pages (from-to)147-152
Number of pages6
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number1
Publication statusPublished - Jan 1 2000


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Physics and Astronomy(all)

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