Numerical study of the TAP equations for infinite-range spin glass models

The nature of spin glass phase for infinite-range model is investigated by an approach without relying on the replica method. Mean field equations are solved numerically and order parameters such as q(x) are obtained. First, to study a kind of quantum effects, the SK model in a transverse field is investigated within the pair approximation. The nature of the spin glass phase is shown to be unchanged by the presence of a transverse field. Secondly, a generalized SK model with a crystal field is studied to clarify the nature of the first order transition. The first order spin glass transition is described consistently. The distribution of pi = 〈S2i〉 is doubly peaked in the spin glass phase on the first order transition line.