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Gauge transformations of the random Ising model are shown to be useful in obtaining rigorous results on thermodynamic quantities. In a restricted region of the phase diagram, we obtain the exact value of the internal energy, rigorous upper bound to the specific heat and a few rigorous relations concerning the correlation functions. In particular it is pointed out that the phase boundary between the paramagnetic and ferromagnetic phases has a singular shape if the spin glass phase does not exist.
Hidetoshi Nishimori (Thu,) studied this question.