Rigorous solution of a mean field spin glass model

[摘要] A separable spin glass model whose exchange integral takes the formJij=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 functionC(t)with respect to the quenched random variablesξis carefully investigated, and it is proved that the related excluded null set𝒩is independent oft. 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 whenξassumes a Gaussian distribution.

[学科分类] 应用数学