Nonperturbative fluctuations and metastability in a simple model: from observables to microscopic theory and back

Understand

Slow dynamics in glassy systems is often interpreted as due to thermally activated events between "metastable" states.

• This emphasizes the role of nonperturbative fluctuations, which is especially dramatic when these fluctuations destroy a putative phase transition predicted at the mean-field level.
• To gain insight into such hard problems, we consider the implementation of a generic back-and-forth process, between microscopic theory and observable behavior via effective theories, in a toy model that is simple enough to allow for a thorough investigation: the one-dimensional $\varphi^4$ theory at low temperature.
• We consider two ways of restricting the extent of the fluctuations, which both lead to a nonconvex effective potential (or free energy) : either through a finite-size system or by means of a running infrared cutoff within the nonperturbative Renormalization Group formalism.