Slow cooling dynamics of the Ising $p$-spin interaction spin-glass model

TL;DR

This paper investigates the slow cooling dynamics and phase transition behavior of the infinite-range Ising p-spin spin-glass model, revealing continuous and discontinuous transitions, and analyzing the non-ergodic phase below the transition.

Contribution

It provides a detailed analysis of the dynamical behavior and phase transitions of the p-spin model, including the slow cooling approach and the nature of the response functions.

Findings

Transition is continuous at high fields, discontinuous at lower fields.

The dynamic critical exponent decreases to zero approaching the tricritical point.

No evidence of a second phase transition within the non-ergodic phase.

Abstract

We have studied dynamical behaviour of the infinite-range Ising spin glass model with $p$-spin interaction above and below the transition into the non-ergodic phase. The transition is continuous at sufficiently high external magnetic field. The dynamic critical exponent of the power-law decay of the autocorrelation function at the transition point is shown to decrease smoothly to zero as the field approaches the ``tricritical'' point from above; at lower fields the transition is discontinuous. The {\it slow cooling} approach is used to study the nonergodic behavior below the transition at zero external field. It is shown that the anomalous response function $\Delta(t,t')$ contains $\delta$-function as well as regular contributions at {\it any} temperature below the phase transition. No evidence of the second phase transition (known to exist within the static replica solution of the same model) is found. At lower enough temperatures the {\it slow cooling} solution approaches the one known for the standard SK model.