Internal Energy, Specific Heat and Correlation Function of the Bond-Random Ising Model

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.