Luca Leuzzi — CNR-NANOTEC, Istituto di Nanotecnologia, Sede di Roma, Piazzale A. Moro 5 #
Logarithmic critical slowing down in complex systems: replica field theory from statics to dynamics in #
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.