Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 2, Pages 147-160

Rigorous solution of a mean field spin glass model

T. C. Dorlas1 and J. R. Wedagedera2

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 Jij=J(ξi1ξj2+ξi2ξj1) which was solved by van Hemmen et al. [12] using large deviation theory [14] is rigorously treated. The almost sure convergence criteria associated with the cumulant generating function C(t) with respect to the quenched random variables ξ is carefully investigated, and it is proved that the related excluded null set 𝒩 is independent of t. 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 ξ assumes a Gaussian distribution.