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Spherical Model as the Limit of Infinite Spin Dimensionality

by: H. E. Stanley
Physical Review Online Archive (Prola), Vol. 176, No. 2. (10 Dec 1968), pp. 718-722, doi:10.1103/physrev.176.718  Key: citeulike:3286366

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Abstract

The Berlin-Kac spherical model (or"spherical approximation to the Ising model") HSM=-JΣ〈ij〉μiμj, with Σj=1Nuj2=N, is found to be equivalent to the ν→∞ limit of the Hamiltonian H(ν)=-JΣ〈ij〉Si(ν)·Sj(ν), where Si(ν) are isotropically interacting ν-dimensional classical spins.


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