THE FREE-ENERGY OF THE RANDOM ISING-MODEL ON THE BETHE LATTICE

The free energy of the +/- J model at finite temperatures on the Bethe lattice was obtained to be beta-F = (1 - 1/2z) integral-infinity/-infinity (1/2x) cosech(pi-x/2-beta)[S(x)]z dx + 1/2z integral-infinity/-infinity [cos(J0x)/2x] x cosech(pi-x/2-beta)[S(x)]z-1 dx, where S(x) is the Fourier transform of the distribution function g(h) of the single-bond effective field h. A tentative self-consistent S(x) gives the spin-glass transition temperature and the energy at T = 0 exactly.