Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 2, Pages 147-160
Rigorous solution of a mean field spin glass model
1University of Wales Swansea, Department of Mathematics, Swansea SA2 8PP, UK
2University of Ruhuna, Department of Mathematics, Matara, Sri Lanka
Received 1 March 1998; Revised 1 December 1999
Copyright © 2000 T. C. Dorlas and J. R. Wedagedera. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A separable spin glass model whose exchange integral takes the form
which was solved by van Hemmen et al. 
using large deviation theory  is rigorously treated. The almost sure
convergence criteria associated with the cumulant generating function
with respect to the quenched random variables is carefully investigated,
and it is proved that the related excluded null set is independent of .
The free energy and hence the other thermodynamic quantities are rederived using Varadhan's Large Deviation Theorem. A simulation is also
presented for the entropy when assumes a Gaussian distribution.