Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 2, Pages 147-160
doi:10.1155/S1048953300000162
Abstract
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.