CRITICAL-TEMPERATURE FOR 2-DIMENSIONAL ISING FERROMAGNETS WITH QUENCHED BOND DISORDER

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(2 J1/kTc) sinh(2 J2/kTc) = 1. Sincec(B) = 1/2, we can take J2 → 0 and use Bergstresser-type inequalities to obtain (ρ/ρdp) exp(-2 J1/kTc|p=pc + = 1, in agreement with Bergstresser's rigorous result for the diluted ferromagnet near the percolation threshold. © 1978 Plenum Publishing Corporation.