Logarithmic critical slowing down in complex systems: From statics to dynamics

This is the authors' abstract. We don't add key points for this paper.

We consider second-order phase transitions in which the order parameter is a replicated overlap matrix. We focus on a tricritical point that occurs in a variety of mean-field models and that, more generically, describes higher-order liquid-liquid or liquid-glass transitions. We show that the static replicated theory implies slowing down with a logarithmic decay in time. The dynamical equations turn out to be those predicted by schematic mode-coupling theory for supercooled viscous liquids at a A₃ singularity, where the parameter exponent is λ=1. We obtain a quantitative expression for the parameter μ of the logarithmic decay in terms of cumulants of the overlap, which are physically observable in experiments or numerical simulations.