Gradient descent dynamics in the mixed p-spin spherical model: finite-size simulations and comparison with mean-field integration

We perform numerical simulations of a long-range spherical spin glass with two and three body interaction terms. We study the gradient descent dynamics and the inherent structures found after a quench from initial conditions well thermalized at temperature T-in. In very large systems, the dynamics perfectly agrees with the integration of the mean-field dynamical equations. In particular, we confirm the existence of an onset initial temperature, within the liquid phase, below which the energy of the inherent structures undoubtedly depends on T-in. This behavior is in contrast with that of pure models, where there is a 'threshold energy' that attracts all the initial configurations in the liquid. Our results strengthen the analogy between mean-field spin glass models and supercooled liquids.

Automated summary

Numerical simulations of a long-range spherical spin glass with two and three body interaction terms show that in very large systems, the dynamics perfectly agrees with the integration of the mean-field dynamical equations. The energy of the inherent structures in the liquid phase depends on an onset initial temperature, which contrasts with that of pure models. These results strengthen the analogy between mean-field spin glass models and supercooled liquids.