Dynamical Replica Theory for Disordered Spin Systems
arXiv:cond-mat/9507101 · doi:10.1103/PhysRevB.53.8184
Abstract
We present a new method to solve the dynamics of disordered spin systems on finite time-scales. It involves a closed driven diffusion equation for the joint spin-field distribution, with time-dependent coefficients described by a dynamical replica theory which, in the case of detailed balance, incorporates equilibrium replica theory as a stationary state. The theory is exact in various limits. We apply our theory to both the symmetric- and the non-symmetric Sherrington-Kirkpatrick spin-glass, and show that it describes the (numerical) experiments very well.
7 pages RevTex, 4 figures, for PRL
References in corpus (5)
- On the Out of Equilibrium Relaxation of the Sherrington - Kirkpatrick model
- Full dynamical solution for a spherical spin-glass model
- Evidence of aging in mean-field spin glass models
- Order Parameter Flow in the SK Spin-Glass I: Replica Symmetry
- Closure of Macroscopic Laws in Disordered Spin Systems: A Toy Model
Cited by in corpus (17)
- A thermal model for adaptive competition in a market
- Dynamic mean-field and cavity methods for diluted Ising systems
- Dynamics of Learning with Restricted Training Sets I: General Theory
- A message-passing scheme for non-equilibrium stationary states
- Inference of kinetic Ising model on sparse graphs
- Correlated fluctuations in strongly-coupled binary networks beyond equilibrium
- Time Dependent Local Field Distribution and Metastable States in the SK-Spin-Glass
- Closure of the Monte Carlo dynamical equations in the spherical Sherrington-Kirkpatrick model
- Pattern-recalling processes in quantum Hopfield networks far from saturation
- Analytical solution of the Monte Carlo dynamics of a simple spin-glass model
- Dynamics of asymmetric kinetic Ising systems revisited
- Statics and dynamics of the Lebwohl-Lasher model in the Bethe approximation
- Finite Size Effects in Separable Recurrent Neural Networks
- Deterministic flows of order-parameters in stochastic processes of quantum Monte Carlo method
- Improved mean-field dynamical equations are able to detect the two-steps relaxation in glassy dynamics at low temperatures
- High-Temperature Dynamics of Spin Glasses
- From random point processes to hierarchical Cavity Master Equations for the stochastic dynamics of disordered systems in Random Graphs: Ising models and epidemics