To Maximize or Not to Maximize the Free Energy of Glassy Systems

The static free energy of glassy systems can be expressed in terms of the Parisi order parameter function. When this function has a discontinuity, the location of the step is determined by maximizing the free energy. In dynamics a transition is found at larger temperature, while the location of the step satisfies a marginality criterion. It is shown here that in a replica calculation this criterion minimizes the free energy. This leads to genuine first order phase transitions with finite latent heat, at the dynamic transition point. Though the order parameter function is the same as in the long-time limit of a dynamical analysis, the thermodynamics is different.