Physical Review B
The annealed Ising magnet on percolation clusters is studied by means of a mapping into a Potts-Ising model and with the Migdal-Kadanoff renormalization-group method. The phase diagram is determined in the three-dimensional parameter space of the Ising coupling K, the bond-occupation probability p, and the fugacity q, which controls the number of clusters. Three phases are identified: percolating ferromagnetic, percolating paramagnetic, and nonpercolating paramagnetic. For large q the phase diagram includes a multicritical point at the intersection of the Ising critical line and the percolation critical line. In the case of random bond percolation (q = 1) the Ising critical line is: p(1 - e-2K) = 1 - exp(- 2L(C)), where Lc is the pure-Ising-model critical coupling.
Kaufman, Miron; Berger, T.; Gujrati, P. D.; and Bowman, D., "Phase Diagram of the Ising Model on Percolation Clusters" (1994). Physics Faculty Publications. 5.
Kaufman, Miron, T. Berger, P. D. Gujrati, and D. Bowman. "Phase Diagram of the Ising Model on Percolation Clusters." Physical Review B 49 (1994): 9583-9585.
Copyright 1994 American Physical Society. Available on publisher's site at http://link.aps.org/doi/10.1103/PhysRevB.49.9583.