The Parisi formula completed

Details The Parisi formula completed The Parisi formula completed

2007-11-11

arxiv.org/abs/0711.1648v1

Phys. Rev. B 77, 104417 (2008)

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

10.1103/PhysRevB.77.104417

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.

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