The Aizenman-sims-starr Scheme for the Sk Model with Multidimensional Spins
نویسنده
چکیده
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 Gärtner-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 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.
منابع مشابه
The Aizenman-Sims-Starr and Guerra’s schemes for the SK model with multidimensional spins
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