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The Aizenman-Sims-Starr scheme for the SK model with multidimensional spins | | Anton Bovier
; Anton Klimovsky
; | | Date: |
14 Nov 2007 | | Abstract: | The non-hierarchical correlation structure of the Sherrington-Kirkpatrick
(SK) model with multidimensional (e.g. Heisenberg) spins is studied at the
level of the logarithmic asymptotic of the corresponding sum of the correlated
exponentials -- the thermodynamic pressure. For this purpose an abstract
quenched large deviations principle (LDP) of 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 ($ ext{AS}^2$
scheme) is extended to the case of the SK model with multidimensional spins.
This extension, based the quenched LDP, shows how the Hadamard matrix products
arise rigorously in the context of the Parisi formula. This allows one to
relate the pressure of the non-hierarchical SK model with the pressure of the
hierarchical GREM by a saddle-point variational formula of the Parisi type
including a negative remainder term. | | Source: | arXiv, 0711.2286 | | Services: | Forum | Review | PDF | Favorites | |
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