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

Peter Lajko·Ferenc Igloi
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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, $ξ_L$, for different widths of the strip, $L \le 21$. The ratio of the two lengths, $ξ_L/L=A$, is found to approach the universal value, $A=2/π$ 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 $η_{\parallel}=1$.

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Peter Lajko, Ferenc Igloi. 1999-08-26. Correlation length-exponent relation for the two-dimensional random Ising model. https://doi.org/10.1103/physreve.61.147

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