Antares Chen University of Chicago
We revisit our geometric interpretation of the Parisi equations via a few interactive demos. We then discuss the historical origins of the Parisi Variational Principle via the Replica method. We demonstrate calculations leading to the action integral form of the replicated free energy, setting us up to introduce Replica Symmetry Breaking next time.
We spent most of our time discussing geometric intuition for the dynamics described by the Parisi’s PDEs.
The equations are given as
When a change of variable is performed
The behavior of this dynamic can be interpreted as follows. At time
On the other hand,
This picture was helpful to have. It plots the evolution of
where, on the right, the red contour corresponds to
When thinking of