Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Volume 2023, Issue 12, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1742-5468/ad0f90
Keywords
cavity and replica method; ergodicity breaking; slow relaxation; glassy dynamics; aging; spin glasses
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In this study, we investigate the stochastic relaxation dynamics of the Ising p-spin model on a random graph. We introduce a new closure scheme for the master equation and propose a solution to the problem of short relaxation timescale in the low-temperature regime. The results are in good agreement with extensive Monte Carlo simulations.
We study the stochastic relaxation dynamics of the Ising p-spin model on a random graph, which is a well-known model with glassy dynamics at low temperatures. We introduce and discuss a new closure scheme for the master equation governing the continuous-time relaxation of the system, which translates into a set of differential equations for the evolution of local probabilities. The solution to these dynamical mean-field equations describes the out-of-equilibrium dynamics at high temperatures very well, notwithstanding the key observation that the off-equilibrium probability measure contains higher-order interaction terms not present in the equilibrium measure. In the low-temperature regime, the solution to the dynamical mean-field equations shows the correct two-step relaxation (a typical feature of glassy dynamics), but with a too-short relaxation timescale. We propose a solution to this problem by identifying the range of energies where entropic barriers play a key role and defining a renormalized microscopic timescale for the dynamical mean-field solution. The final result perfectly matches the complex out-of-equilibrium dynamics computed through extensive Monte Carlo simulations.
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