Abstract
The configuration-averaged free energy of a quenched, random bond Ising model on a square lattice which contains an equal mixture of two types of ferromagnetic bonds J1 and J2 is shown to obey the same duality relation as the ordered rectangular model with the same two bond strengths. If the random.system has a single, sharp critical point, the critical temperature Tc must be identical to that of the ordered system, i.e., sinh(2J 1/kT c) sinh(2J 2/kT c) = 1. Since (B)c = 1/2, we can takeJ 2 → 0 and use Bergstresser-type inequalities to obtain(ρ/ρdp) exp(−2J 1/kTc¦p=pc + = 1, in agreement with Bergstresser's rigorous result for the diluted ferromagnet near the percolation threshold.
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References
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Work supported in part by National Science Foundation Grant No. DMR 76-21703, Office of Naval Research Grant No. N00014-76-C-0106, and National Science Foundation MRL program Grant No. DMR 76-00678.
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Fisch, R. Critical temperature for two-dimensional ising ferromagnets with quenched bond disorder. J Stat Phys 18, 111–114 (1978). https://doi.org/10.1007/BF01014302
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DOI: https://doi.org/10.1007/BF01014302