Distribution of spins and the thermodynamic properties in the glass-like (spin glass) phase of random Ising bond models

The distribution of spins and the thermodynamic properties of random Ising bond models are obtained by the use of the integral equation for the distribution function of the effective fields g(l). The integral equation is derived for a general case in a simple way by the use of the Bethe approximation. From the relation between the magnetisation and the effective field, the phase boundaries between the paramagnetic phase, the glass-like (spin glass) phase (GLP) and the ferromagnetic phase are obtained for the general distribution P(J). For a binary mixture with J A =-J B , z=3, the integral equation is solved by approximating g(l) by a superposition of the delta functions. The specific heat and the susceptibility have cusps at the temperature T G , below which the glass-like phase appears.