Understanding Vogel-Fulcher–like equilibration times through the partial equilibration scenario

¹ Tata Institute of Fundamental Research-Hyderabad - Hyderabad, Telangana 500046, India
² Institute of Aeronautical Engineering - Hyderabad, Telangana 500043, India
³ Department of Physics, Central University of Rajasthan - Bandar Sindri, Rajasthan 305817, India

^(a) E-mail: shankaraiahnaddi@gmail.com (corresponding author)

Received: 5 December 2022
Accepted: 17 April 2023

Abstract

We test a post-quench Partial Equilibration Scenario (PES) of Ritort and colleagues, through Monte Carlo quench simulations, of a vector-spin model for a cubic-to-tetragonal, martensitic structural transition. We confirm the PES signature distribution of an exponential tail in heat releases, scaled in an effective search temperature that regulates energy-lowering passages between fixed-energy shells. Our simulations find that this effective temperature vanishes linearly in the deviation of the quench temperature from a divergence temperature, where passage bottlenecks in phase space segment their topology, and entropy barriers diverge. Equilibration delay times, exponential in the inverse effective temperature, are thus predicted to show singular Vogel-Fulcher behaviour, understood here as an arrest of PES heat releases to the bath, and confirmed by experimental data on martensitic alloys.