Memory effect and phase transition in a hierarchical trap model for spin glass

TL;DR

This paper introduces a hierarchical trap model and a novel dynamical tree method to study memory effects and phase transitions in spin glasses, revealing the connection between structure and glassy dynamics.

Contribution

The paper presents the first explicit demonstration of memory effects in a hierarchical energy landscape using a new dynamical tree method.

Findings

Reproduces nontrivial waiting-time and waiting-temperature dependences.

Shows a structural phase transition coincides with the onset of condensation.

Highlights the role of hierarchical structure in glassy behavior.

Abstract

We introduce an efficient dynamical tree method that enables us, for the first time, to explicitly demonstrate thermo-remanent magnetization memory effect in a hierarchical energy landscape. Our simulation nicely reproduces the nontrivial waiting-time and waiting-temperature dependences in this non-equilibrium phenomenon. We further investigate the condensation effect, in which a small set of micro-states dominates the thermodynamic behavior, in the multi-layer trap model. Importantly, a structural phase transition of the tree is shown to coincide with the onset of condensation phenomenon. Our results underscore the importance of hierarchical structure and demonstrate the intimate relation between glassy behavior and structure of barrier trees.