The sphericalp-spin interaction spin-glass model

The relaxational dynamics for local spin autocorrelations of the sphericalp-spin interaction spin-glass model is studied in the mean field limit. In the high temperature and high external field regime, the dynamics is ergodic and similar to the behaviour in known liquid-glass transition models. In the static limit, we recover the replica symmetric solution for the long time correlation. This phase becomes unstable on a critical line in the (T, h) plane, where critical slowing down is observed with a cross-over to power law decay of the correlation function ∝t−ν, with an exponent ν varying along the critical line. For low temperatures and low fields, ergodicity in phase space is broken. For small fields the transition is discontinuous, and approaching this transition from above, two long time scales are seen to emerge. This dynamical transition lies at a somewhat higher temperature than the one obtained within replica theory. For larger fields the transition becomes continuous at some tricritical point. The low temperature phase with broken ergodicity is studied within a modified equilibrium theory and alternatively for adiabatic cooling across the transition line. This latter scheme yields rather detailed insight into the formation and structure of the ergodic components.