Minimal cooling speed for glass transition in a simple solvable energy landscape model

TL;DR

This paper derives the minimal cooling speed needed to form a glass in a simple solvable energy landscape model, linking it to relaxation times and thermal history, and verifies results with simulations.

Contribution

It introduces a solvable energy landscape model that captures glass transition and crystallization, providing analytical expressions for minimal cooling speed.

Findings

Minimal cooling speed depends on relaxation time and thermal history.

Thermal history influences fluctuations near the glass transition.

Analytical results are confirmed by kinetic Monte-Carlo simulations.

Abstract

The minimal cooling speed required to form a glass is obtained for a simple solvable energy landscape model. The model, made from a two-level system modified to include the topology of the energy landscape, is able to capture either a glass transition or a crystallization depending on cooling rate. In this setup, the minimal cooling speed to achieve glass formation is then found to be related with the relaxation time and with the thermal history. In particular, we obtain that the thermal history encodes small fluctuations around the equilibrium population which are exponentially amplified near the glass transition, which mathematically corresponds to the boundary layer of the master equation. Finally, to verify our analytical results, a kinetic Monte-Carlo simulation was implemented.