Frequency-domain study of relaxation in a spin glass model for the structural glass transition

TL;DR

This study analyzes the frequency-dependent relaxation behavior in a spin glass model related to the structural glass transition, revealing scaling laws and Vogel-Fulcher behavior near the critical temperature.

Contribution

It demonstrates that the finite-size mean-field ROM exhibits glass-like susceptibility scaling and Vogel-Fulcher law behavior consistent with experimental observations.

Findings

Imaginary susceptibility follows glass-forming liquid scaling forms.

Peak frequency decreases with temperature following Vogel-Fulcher law.

Critical temperature aligns with the vanishing of configurational entropy.

Abstract

We have computed the time-dependent susceptibility for the finite-size mean-field Random Orthogonal model (ROM). We find that for temperatures above the mode-coupling temperature the imaginary part of the susceptibility $\chi''(\nu)$ obeys the scaling forms proposed for glass-forming liquids. Furthermore, as the temperature is lowered the peak frequency of $\chi''$ decreases following a Vogel-Fulcher law with a critical temperature remarkably close to the known critical temperature $T_c$ where the configurational entropy vanishes.