Relaxation Spectra at the Glass Transition: Origin of Power Laws

TL;DR

This paper introduces a dynamical model for the glass transition based on a frustrated spin system, explaining the emergence of power-law relaxation spectra near the transition.

Contribution

It presents a simple, analytically tractable model linking free-energy landscape curvature to glassy relaxation spectra, supported by numerical simulations.

Findings

Response evolves from Debye peak to power-law behavior

Analytical form for response function derived

Numerical Langevin simulations confirm theoretical predictions

Abstract

We propose a simple dynamical model of the glass transition based on the results from a non-randomly frustrated spin model which is known to form a glassy state below a characteristic quench temperature. The model is characterized by a multi-valleyed free-energy surface which is modulated by an overall curvature. The transition associated with the vanishing of this overall curvature is reminiscent of the glass transition. In particular, the frequency-dependent response evolves from a Debye relaxation peak to a function whose high-frequency behavior is characterized by a non-trivial power law. We present both an analytical form for the response function and numerical results from Langevin simulations.