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

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 ${\chi }^{\mathrm{\prime }\mathrm{\prime }}(\nu )$ obeys the scaling forms proposed for glass-forming liquids. Furthermore, as the temperature is lowered the peak frequency of ${\chi }^{\mathrm{\prime }\mathrm{\prime }}$ decreases following a Vogel-Fulcher law with a critical temperature remarkably close to the known critical temperature $T_c$ where the configurational entropy vanishes.