Frequency-domain study of $\alpha$-relaxation in the Random Orthogonal Model

TL;DR

This study numerically analyzes the frequency-dependent susceptibility in the finite-size Random Orthogonal Model, revealing glass-like relaxation behavior and scaling consistent with experimental observations near the critical temperature.

Contribution

It provides the first detailed frequency-domain analysis of $eta$-relaxation in the ROM, linking it to glassy dynamics and critical temperature behavior.

Findings

Susceptibility $ ext{Im}( u)$ follows a glass-forming liquid scaling form.

Peak frequency decreases with temperature, following Vogel-Fulcher law.

Critical temperature close to where configurational entropy vanishes.

Abstract

The time-dependent susceptibility for the finite-size mean-field Random Orthogonal model (ROM) is studied numerically for temperatures above the mode-coupling temperature. The results show that the imaginary part of the susceptibility $\chi''(\nu)$ obeys the scaling form proposed for glass-forming liquids with the peak frequency decreasesing as the temperature is lowered consistently with the Vogel-Fulcher law with a critical temperature remarkably close to the known critical temperature $T_c$ of the model where the configurational entropy vanishes.