Low-temperature behaviour of the random-field Ising model

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Abstract
The random-field Ising model, with a normally distributed random field, is considered for systems with large, but finite, coordination number z. The conventional loop expansion is shown to fail below a temperature T* approximately=Tc/z, where Tc is the (ferromagnetic) transition temperature of the pure system. Resummation of the most divergent terms in the expansion yields a specific heat anomaly in the temperature region T<or approximately=T*. It is conjectured that the temperature T* has dynamical significance.