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

Péter Lajkó, F. Iglói

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We consider the two-dimensional (2D) random Ising model on a diagonal strip of the square lattice, where the bonds take two values. J1 <J2, 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 ξL for different widths of the strip L ≤ 21. The ratio of the two lengths ξL/L = A is found to approach the universal value A = 2/π for large L, independent of the dilution parameter J1/J2. 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 η = 1.

Original languageEnglish
Pages (from-to)147-152
Number of pages6
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume61
Issue number1
Publication statusPublished - Jan 2000

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Correlation Length
Ising model
Ising Model
Strip
strip
Exponent
exponents
Critical Temperature
Square Lattice
triangles
Averaging
dilution
Correlation Function
Triangle
Critical point
Star
critical point
critical temperature
Decay
Iteration

ASJC Scopus subject areas

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

Cite this

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