  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 $A_3$ singularity, where the parameter
exponent is $\lambda=1$. We obtain a quantitative expression for the parameter
$\mu$ of the logarithmic decay in terms of cumulants of the overlap, which are
physically observable in experiments or numerical simulations.
