SLOW COOLING DYNAMICS OF THE ISING P-SPIN INTERACTION SPIN-GLASS MODEL

We have studied the dynamical behavior of the infinite-range Ising spi n-glass model with p-spin interaction above and below the transition i nto the nonergodic phase. The transition is continuous at sufficiently high external magnetic field. The dynamic critical exponent of the po wer-law decay of the autocorrelation function at the transition point is shown to decrease smoothly to zero as the field approaches the <<tr icritical>> point from above; in weaker fields the transition is disco ntinuous, The slow-cooling approach is used to study the nonergodic be havior below the transition at zero external field. it is shown that t he anomalous response function Delta(t, t') contains delta-function as well as regular contribution at any temperature below the phase trans ition. No evidence of the second phase transition (known to exist with in the static replica solution of the same model) is found. At low eno ugh temperatures the slow-cooling solution approaches the one known fo r the standard Sherrington-Kirkpatrik model.