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 meanfield random orthogonal model (ROM). We find that for temperatures above the mode-coupling temperature, the imaginary part of the susceptibility χ′′(ν) obeys the scaling forms proposed for glass-forming liquids. Furthermore, as the temperature is lowered the peak frequency of χ′′ decreases, following a Vogel-Fulcher law with a critical temperature remarkably close to the known critical temperature Tc, where the configurational entropy vanishes. A model Hamiltonian or an effective Lagrangian capable of describing relaxation processes in supercooled liquids and structural glasses is difficult to obtain. However, starting with the work of Kirkpatrick, Thirumalai and Wolynes [1, 2] in the late ’80s, it is now clear that there is a close analogy between some mean-field spin-glass models and structural glasses [3]. The former thus provide a set of microscopical models where glassy dynamics can be studied analytically. The basic simplification occurring in mean-field models is that after averaging over the disorder and making the number of spin very large (N → ∞) one is left with a closed set of equations for the two-time correlation and response functions which, above a critical temperature, are basically equivalent to the schematic mode-coupling equations introduced by Leutheusser, Götze and others [4] as a model for the ideal glass transition. In mean-field models the barrier separating different ergodic components diverges in the mean-field limit, hence at the critical temperature TD a real ergodic to non-ergodic transition takes place with diverging relaxation times since barriers cannot be overcome, in agreement with mode-coupling theories (MCT) where TD coincides with the MCT critical temperature TMCT. In what follows we will denote TD by TMCT. In real systems, TMCT still denotes the separation temperature for activated hopping-dominated dynamics [5]; however, barriers are of finite height and the glass transition appears at Tg < TMCT, where the typical activation