Abstract
We propose a theory for the site-diluted Ising model which is an extension to disordered systems of the self-consistent Ornstein-Zernike approximation of Hoye and Stell. By using the replica method in the context of liquid-state theory, we treat the concentration of impurities as an ordinary thermodynamic variable. This approach is not limited to the weak-disorder regime or to the vicinity of the percolation point. A preliminary analysis using series expansion shows that it can predict accurately the dependence of the critical temperature on dilution and can reproduce the nonuniversal behavior of the effective exponents. The theory also gives a reasonable estimate of the percolation threshold.
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Kierlik, E., Rosinberg, M.L. & Tarjus, G. A self-consistent Ornstein-Zernike approximation for the site-diluted Ising model. J Stat Phys 89, 215–232 (1997). https://doi.org/10.1007/BF02770762
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DOI: https://doi.org/10.1007/BF02770762