Rigorous solution of a mean field spin glass model. (2000)

• Record Type: Journal Article
• Authors: Dorlas, T. C.; Wedagedera, J. R.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 13:Number 2(2000)
• Page Start: 147
• Page End: 160
• Publication Date: 2000
• Subjects: spin glass -- large deviations -- egodicity; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953300000162
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : A separable spin glass model whose exchange integral takes the form J i j = J ( ξ i 1 ξ j 2 + ξ i 2 ξ j 1 ) 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.