Phys. Rev. B 77, 104417 (2008) [5 pages]Free-energy functional for the Sherrington-Kirkpatrick model: The Parisi formula completedReceived 6 February 2008; published 13 March 2008 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. © 2008 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevB.77.104417
DOI:
10.1103/PhysRevB.77.104417
PACS:
75.50.Lk, 64.60.Cn
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