Spherical Model as the Limit of Infinite Spin Dimensionality

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10 December 1968

journal article
research article
Published by American Physical Society (APS) in Physical Review B

Vol. 176 (2) , 718-722
https://doi.org/10.1103/physrev.176.718

Abstract

The Berlin-Kac spherical model (or"spherical approximation to the Ising model")

H^{SM} = - J Σ \overset{}{〈 ij 〉} μ_{i} μ_{j}, with Σ \overset{N}{j = 1} {u_{j}}^{2} = N,

is found to be equivalent to the

ν \to \infty

limit of the Hamiltonian

H^{(ν)} = - J Σ \overset{}{〈 ij 〉} {S_{i}}^{(ν)} \cdot {S_{j}}^{(ν)},

where

{S_{i}}^{(ν)}

are isotropically interacting

ν

-dimensional classical spins.

Keywords

This publication has 7 references indexed in Scilit:

Dependence of Critical Properties on Dimensionality of Spins
Physical Review Letters, 1968
Critical Correlations in the Ising Model
Physical Review B, 1967
Possibility of a Phase Transition for the Two-Dimensional Heisenberg Model
Physical Review Letters, 1966
ON THE MATHEMATICAL MECHANISM OF PHASE TRANSITION
Proceedings of the National Academy of Sciences, 1966
The work of T.H. Berlin in statistical mechanics …a personal reminiscence
Physics Today, 1964
The Spherical Model of a Ferromagnet
Physical Review B, 1952
An analytical approach to the ising problem
Communications on Pure and Applied Mathematics, 1951