Résumé
The overlap between liquid configurations is at the core of the mean-field description of the glass transition, corresponding to the order parameter for the thermodynamic liquid-to-glass phase transition. More generally, the overlap (or similarity) between the microscopic degrees of freedom of two copies (or replicas) of a system represents an insightful concept when studying disordered systems evolving in rugged free-energy landscapes. In this talk, I will introduce the notion of overlap and emphasize the connection between its probability distribution and the structure of the underlying rough landscape. I will then review methods to measure the overlap probability distribution in computer simulations of realistic systems via biased sampling techniques, with most examples taken from glass transition studies. Experimental determinations of the overlap are notoriously more challenging because microscopic degrees of freedom are not usually accessible and will be mentioned in the concluding part of the talk.