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

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-tetragonal, martensitic structural transition. We confirm the PES signature distribution of an exponential tail in heat releases, scaled in an effective search temperature that controls energy-lowering passages between fixed-energy shells. Our simulations find that this effective temperature vanishes linearly in the deviation of the quench temperatures from a characteristic temperature, where passage bottlenecks in phase space change their topology, and entropy barriers diverge. Equilibration delay times, exponential in the inverse effective temperature, are thus predicted to show singular Vogel-Fulcher behaviour, that is now understood as an arrest of PES heat releases to the bath, and confirmed in experimental data on martensitic alloys.