×

High temperature regime for a multidimensional Sherrington-Kirkpatrick model of spin glass. (English) Zbl 0906.60077

Summary: F. Comets and J. Neveu have initiated [Commun. Math. Phys. 166, No. 3, 549-564 (1995; Zbl 0811.60098)] a method to prove convergence of the partition function of disordered systems to a log-normal random variable in the high temperature regime by means of stochastic calculus. We generalize their approach to a multidimensional Sherrington-Kirkpatrick model with an application to the Heisenberg model of uniform spins on a sphere of \(\mathbb{R}^d\), see [D. Gabay and G. Toulouse, J. Phys. 42, L103–L106 (1981)]. The main tool that we use is a truncation of the partition function outside a small neighbourhood of the typical energy path.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)

Citations:

Zbl 0811.60098
PDFBibTeX XMLCite
Full Text: DOI