Rigorous solution of a mean field spin glass model (Q1580052)

Summary: A separable spin glass model whose exchange integral takes the form \(J_{ij}= J(\xi_{i1} \xi_{j_2}+ \xi_{i2} \xi_{j1})\) which was solved by J. L. van Hemmen et al. using large deviation theory is rigorously treated. The almost sure convergence criteria associated with the cumulant generating function \(C(t)\) with respect to the quenched random variables \(\xi\) is carefully investigated, and it is proved that the related excluded null set \({\mathcal N}\) 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 \(\xi\) assumes a Gaussian distribution.