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.
Highlights
An exactly solvable model of a spin glass which was introduced by van Hemmen et al [12, 13] is studied
Where the i and r/j are i.i.d, random variables with a symmetric distribution with zero mean and variance 1. This model resembles a similar model proposed by Pastur and Figotin in [8,9,10]
In the absence of ferromagnetic coupling and an external magnetic field h, the Hamiltonian can be written as JN({S}, {J}) NJ N- 1
Summary
An exactly solvable model of a spin glass which was introduced by van Hemmen et al [12, 13] is studied. Where co(i)- +1 are N Ising spins interacting with each other in pairs (i, j) and with an external magnetic field h. Where the i and r/j are i.i.d, random variables with a symmetric distribution with zero mean and variance 1. This model resembles a similar model proposed by Pastur and Figotin in [8,9,10]. It was van Hemmen et al who first used a large deviation (LD) argument to successfully solve this model. In the absence of ferromagnetic coupling and an external magnetic field h, the Hamiltonian can be written as JN({S}, {J}) NJ N- 1. (ii) when has a Gaussian distribution, s--.0 as T--0
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