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

Abstract

We consider the two-dimensional (2d) random Ising model on a diagonal strip of the square lattice, where the bonds take two values, $J_1>J_2$, 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, ${\xi }_L$, for different widths of the strip, $L\le 21$. The ratio of the two lengths, ${\xi }_L/L=A$, is found to approach the universal value, $A=2/\pi$ for large $L$, independent of the dilution parameter, $J_1/J_2$. 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 coovariant and the corresponding decay exponent is ${\eta }_{\parallel }=1$.

6 pages RevTex, 5 eps figures included

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Cited by in corpus (6)

• Strong disorder RG approach of random systems
• Critical phenomena at perfect and non-perfect surfaces
• Self-Consistent Scaling Theory for Logarithmic Correction Exponents
• Scaling Analysis of the Site-Diluted Ising Model in Two Dimensions
• Surface critical behavior of random systems at the ordinary transition
• Iterated star-triangle transformation on inhomogeneous 2D Ising lattices