Improved mean-field dynamical equations are able to detect the two-steps relaxation in glassy dynamics at low temperatures
arXiv:2307.00882 · doi:10.1088/1742-5468/ad0f90
Abstract
We study the stochastic relaxation dynamics of the Ising p-spin model on a random graph, 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, that translates into a set of differential equations for the evolution of local probabilities. The solution to these dynamical mean-field equations describes very well the out-of-equilibrium dynamics at high temperatures, 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 the glassy dynamics), but with a relaxation timescale too short. 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.
arXiv comment24 pages, 9 figures
References in corpus (19)
- Theory of Phase Ordering Kinetics
- Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
- The Bethe lattice spin glass revisited
- On the Out of Equilibrium Relaxation of the Sherrington - Kirkpatrick model
- Rigorous Inequalities between Length and Time Scales in Glassy Systems
- Full dynamical solution for a spherical spin-glass model
- A ferromagnet with a glass transition
- Self Induced Quenched Disorder: A Model for the Glass Transition
- On the dynamics of the glass transition on Bethe lattices
- Colloidal glass transition: Beyond mode-coupling theory
- Rethinking mean-field glassy dynamics and its relation with the energy landscape: the awkward case of the spherical mixed p-spin model
- Strong ergodicity breaking in aging of mean field spin glasses
- Approximation schemes for the dynamics of diluted spin models: the Ising ferromagnet on a Bethe lattice
- Dynamical Replica Theory for Disordered Spin Systems
- On weak ergodicity breaking in mean-field spin glasses
- Generalized mode-coupling theory of the glass transition: schematic results at finite and infinite order
- A Cavity Master Equation for the continuous time dynamics of discrete spins models
- Dynamical replica analysis of processes on finitely connected random graphs I: vertex covering
- Exploring the diluted ferromagnetic p-spin model with a Cavity Master Equation