Understanding glass-like Vogel-Fulcher-Tammann equilibration times: microcanonical effective temperatures in quenched 3D martensites

TL;DR

This paper uses Monte Carlo simulations of 3D martensitic transitions to explore how effective temperatures govern slow glass-like equilibration times, revealing a Vogel-Fulcher divergence near a freezing temperature.

Contribution

It demonstrates that a partial equilibration scenario explains the Vogel-Fulcher divergence of equilibration times in quenched martensitic systems through effective temperature analysis.

Findings

Effective search temperature scales linearly with (T_d - T).

Heat release distributions show exponential tails consistent with PES.

Equilibration times diverge as e^{1/(T_d - T)} near T_d.

Abstract

We do Monte Carlo simulations of four 3D structural transitions, with vector-spin models of their martensitic strain domains under quenches to $T$, to test a generic post-quench Partial Equilibration Scenario (PES) of Ritort. We indeed confirm that energy-lowering passages between fixed-energy shells induce a signature PES distribution of an exponential tail in heat releases, scaled in an effective search temperature. A linear vanishing of this $T_{eff}(T)\sim T_d -T$ at a temperature $T_d$ where PES passage-searches freeze, explains the Vogel-Fulcher like divergence of equilibration times $ e^{1/ T_{eff} (T)}\sim e^{1/(T_d -T)}$, extracted from incubation-time delays of simulations and martensitic alloys.