Quasi-deterministic dynamics, memory effects, and lack of self-averaging in the relaxation of quenched ferromagnets

Abstract

We discuss the interplay between the degree of dynamical stochasticity, memory persistence and violation of the self-averaging property in the aging kinetics of quenched ferromagnets. We show that, in general, the longest possible memory effects, which correspond to the slowest possible temporal decay of the correlation function, are accompanied by the largest possible violation of self-averaging and a quasi-deterministic descent into the ergodic components. This phenomenon is observed in different systems, such as the Ising model with long-range interactions, including mean-field, and the short-range random field Ising model.

arXiv commentIntroduction strongly revised, changed figures. Accepted for publication as a Rapid Communication in Physical Review E

References in corpus (17)

• Theory of Phase Ordering Kinetics
• Statistical mechanics and dynamics of solvable models with long-range interactions
• Growth Laws for Phase Ordering
• Phase Ordering Kinetics of One-Dimensional Non-Conserved Scalar Systems
• Crossover in Growth Law and Violation of Superuniversality in the Random Field Ising Model
• Slow relaxation in the large N model for phase ordering
• Local scale invariance as dynamical space-time symmetry in phase-ordering kinetics
• Phase ordering kinetics of the long-range Ising model
• Exact Exponent $\lambda$ of the Autocorrelation Function for a Soluble Model of Coarsening
• Dynamics of ferromagnetic spherical spin models with power law interactions: exact solution
• Off equilibrium response function in the one dimensional random field Ising model
• How soon after a zero-temperature quench is the fate of the Ising model sealed?
• One dimensional phase-ordering in the Ising model with space decaying interactions
• Perturbation Expansion in Phase-Ordering Kinetics: I. Scalar Order Parameter
• Universality in the time correlations of the long-range 1d Ising model
• Effective mobility and diffusivity in coarsening processes
• Coarsening Kinetics of a Two Dimensional O(2) Ginzburg-Landau Model: Effect of Reversible Mode Coupling

Cited by in corpus (9)

• Breakdown of Ergodicity and Self-Averaging in Polar Flocks with Quenched Disorder
• Kinetics of the Two-dimensional Long-range Ising Model at Low Temperatures
• Coexistence of coarsening and mean field relaxation in the long-range Ising chain
• Phase-ordering kinetics in the Allen-Cahn (Model A) class: universal aspects elucidated by electrically-induced transition in liquid crystals
• Ordering Kinetics of the two-dimensional voter model with long-range interactions
• Coarsening and metastability of the long-range voter model in three dimensions
• Ordering Dynamics of the Random Field Long-range Ising Model in One Dimension
• Aging properties of the voter model with long-range interactions
• Ordering kinetics with long-range interactions: interpolating between voter and Ising models