Comets and Neveu have initiated in  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 ℝd, see . The main tool that we use is a truncation of the partition function outside a small neighbourhood of the typical energy path.
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Received: 30 October 1996 / In revised form: 13 October 1997
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Toubol, A. High temperature regime for a multidimensional Sherrington–Kirkpatrick model of spin glass. Probab Theory Relat Fields 110, 497–534 (1998). https://doi.org/10.1007/s004400050157
- Mathematics Subject Classification (1991): 60K35