The glass transition (from a liquid to a solid disordered phase) is an ubiquitous phenomenon in condensed matter physics, still lacking  a complete description. A main step in the analysis of a standard phase transition consists of identifying the correct order parameter, allowing  then to construct a Landau functional, first analyzed in term of a mean-field description, and then, eventually, promoted to a truly fluctuating field in order to get a full-fledged theoretical description. Based on the "random first-order transition" (RFOT) theory, the physical order parameter for the glass transition has been identified as the similarity, also called "overlap", between equilibrium configurations (consider this sentence as a simplified summary for a complex situation) . In this description, the liquid to glass transition corresponds to such an overlap jumping from a (nearly) vanishing value (in the liquid phase) to a large value at the transition.

In the last few years a lot of effort has been devoted to develop an effective field theory of glass-forming systems directly formulated in terms of an overlap field. It leads naturally to a scalar field theory in presence of quenched disorder, which can be studied using standard tools of statistical physics, such as the Non Perturbative Renomalization Group.

In this context, we have studied the critical point that terminates the transition line in an extended phase diagram where one introduces a coupling between liquid configurations. We have shown that, in agreement with other recent results, the long-distance physics in the vicinity of this critical point is in the same universality class as that of a paradigmatic disordered model: the random-field Ising model (RFIM). One motivation for studying this specific region of parameters stems from recent numerical works that have directly focused on the behavior of supercooled liquids in the presence of such an attractive coupling and have provided evidence for a first-order transition line and a terminal critical point. In consequence, our predictions are prone to direct tests in the future.

Ref : "Random-Field-like Criticality in Glass-Forming Liquids" G. Biroli, C. Cammarota, G. Tarjus, and M. Tarzia Phys. Rev. Lett. 112, 175701 (2014).