Local magnetic field distributions. III. Disordered systems

We conclude our investigations of the local magnetic field distributions P(h) by examining disordered spin systems. Exact analytical results are given on the Bethe lattice with random bonds and the Sherrington-Kirkpatrick (SK) spin-glass model. Below the spin-glass transition temperature Tg of the SK model, the slope of P(0) as a function of temperature is found to be almost linear, frozen to its value at Tg, in a manner reminiscent of other freezing phenomena found for this model. Simulations on finite-range models appear to show a correlated onset of certain features characteristic of the spin-glass phase of the SK (infinite-range) model but at a temperature higher than any associated with a phase transition.