The Parisi formula completed
Disordered Systems and Neural Networks
2008-09-16 v1 Statistical Mechanics
Abstract
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 . Finally we show without resorting to the replica trick that the solution of the stationarity equations leads to a marginally stable thermodynamic state.
Keywords
Cite
@article{arxiv.0711.1648,
title = {The Parisi formula completed},
author = {V. Janis},
journal= {arXiv preprint arXiv:0711.1648},
year = {2008}
}