Dynamical Phase Transitions and Spin Glasses

By measuring the distance between two configurations subjected to the same thermal noise, one observes for spin glasses three phases: a high-temperature phase (T> T 1), where the distance between the two configurations vanishes in the long-time limit; an intermediate phase (1’~< T < T,), where this distance has a nonzero limit independent of the initial distance; a low-temperature phase (T< ~‘2), where the distance depends on the initial distance. For the 3d and 4d ±I spin glasses, the results of Monte Carlo simulations give clear evidence for the existence of these three phases. For the Sherrington—Kirkpatrick model, T1 is infinite whereas T~is close to the equilibrium transition temperature. For the 2d ±Jspin glass, the behavior at high and low temperature is similar to that of the 3d and 4d models but there is much less evidence for the presence of the intermediate phase and for well-defined transition temperatures between these phases.