From an unconstrained model with quenched interactions to a constrained model with annealed interactions

The frustrated lattice gas model is studied in the quenched version where the interactions are quenched random variables, and in the annealed version where the interactions are allowed to evolve in time with a suitable kinetic constraint. The dynamical nonlinear susceptibility, recently introduced by Donati et al, is evaluated. In the annealed version we observe a behaviour very similar to the results for the p-spin models in mean field, and those for a Lennard-Jones mixture as found by Donati et al. In the quenched version we observe a substantially different behaviour of the dynamical susceptibility. The results suggest that the behaviour of the dynamical susceptibility in the annealed model can be interpreted as the imprint of the thermodynamic transition present in the quenched model and signalled by the divergence of the static nonlinear susceptibility. A similar mechanism might also be present in glassy systems.