Abstract
The replica method is applied to Ising spin systems with random interactions. An effective Hamiltonian is derived for an arbitrary distribution of random bonds and the thermodynamic variational principle is used to evaluate the mean-field free energy. In the general case, the free energy depends explicitly on an infinite set of momenta ((si)k). For specific types of bond randomness results obtained previously are recovered. The phase diagram of the dilute Ising model with competing nearest-neighbour and next-nearest-neighbour interactions is worked out in detail. A spin glass phase is predicted at large enough dilution.

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