Aging Processes within One `Pure State' of the SK Model

TL;DR

This study uses Monte Carlo simulations to explore aging phenomena in the SK model's pure state, revealing a unified interpretation through the growth of quasi-equilibrium domains and the dominance of a single pure state.

Contribution

It introduces the concept of growth of quasi-equilibrium domains to interpret aging phenomena and suggests a dominant pure state spans most of the phase space.

Findings

Rich variety of aging phenomena observed

Unified interpretation via quasi-equilibrium domains

Dominant pure state spans almost entire phase space

Abstract

Monte Carlo simulations on the SK model have been done to investigate aging processes after a rapid quench from $T=\infty$ to the spin-glass phase. The time range of simulations is taken care of so that the system does not surmount free-energy barriers between the pure states which are considered to diverge in the thermodynamic limit. We simulate time evolutions of extensive energy of the system, Parisi's overlap distribution function, auto-correlation and clones-correlation functions, distribution functions of the two correlations, and magnetization induced by the field applied after a certain waiting time. The data simulated exhibit a rich variety of aging phenomena. Most of them can be interpreted in a unified way, though qualitatively, by the scenario of ``growth of quasi-equilibrium domains'' which we will introduce in this work. More surprisingly, they suggest strongly that a basin of attraction of one dominant pure state spans almost an entire phase space of the system with a common time-reversal symmetry.