The Parisi formula completed
Abstract
Description
The Parisi formula for the free energy of the Sherrington-Kirkpatrick model is completed to a closed-form generating functional. We first find an integral representation for a solution of the Parisi differential equation and represent the free energy as a functional of order parameters. Then we set stationarity equations for local maxima of the free energy determining the order-parameter function on interval $[0,1]$. Finally we show without resorting to the replica trick that the solution of the stationarity equations leads to a marginally stable thermodynamic state.