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Preprint 44-2007

The Aizenman-Sims-Starr scheme for the SK model with multidimensional spins

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Author(s) : Anton Bovier , Anton Klimovsky

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 44-2007

MSC 2000

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B44 Disordered systems
60F10 Large deviations

Abstract :
We get non-trivial upper and lower bounds on the thermodynamic pressure of the Sherrington-Kirkpatrick (SK) model with multidimensional (e.g. Heisenberg) spins in terms of an optimum of the corresponding Parisi functional. For this purpose an abstract quenched large deviations principle (LDP) of the Gaertner-Ellis type is obtained under an assumption of measure concentration. With the aid of this principle the framework of the Aizenman-Sims-Starr comparison scheme (AS^2 scheme) is extended to the case of the SK model with multidimensional spins.

Keywords : Sherrington-Kirkpatrick model, multidimensional spins, Aizenman-Sims-Starr scheme, quenched large deviations, concentration of measure, Parisi formula

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