Transfer-matrix scaling for diluted Ising systems

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Abstract
A transfer-matrix scaling technique is developed for randomly diluted systems and applied to the site-diluted Ising model on a square lattice. For each connected configuration between adjacent columns, the contribution of the respective transfer matrix to the decay of correlations is considered only as far as the ratio of the two largest eigenvalues, allowing an economical incorporation of configurational averages. Predictions for the phase boundary at and near the percolation and pure Ising limits, and for the correlation exponent η at those limits, agree with exactly known results to within 1% error with largest strip widths of only L=5. The exponent η remains near the pure value (1/4) for all intermediate concentrations until it turns over to the percolation value at the threshold.