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