Critical behaviour and ultrametricity of Ising spin-glass with long-range interactions

Ising spin-glass systems with long-range interactions (J(r) similar to r(-s igma))are considered. A numerical study of the critical behaviour is presen ted in the non-mean-field region together with an analysis of the probabili ty distribution of the overlaps and of the ultrametric structure of the spa ce of the equilibrium configurations in the frozen phase. Also. in the pres ence of diverging thermodynamical fluctuations at the critical point the be haviour of the model is shown to be of the replica symmetry breaking type a nd there are hints of a non-trivial ultrametric structure. The parallel tem pering algorithm has been used to simulate the dynamical approach to equili brium of such systems.