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The behavior of the spherical model of a ferromagnet with an interaction energy between the magnetic spins which varies with distance as 1{r^d+} (where d is the dimensionality of the lattice and >0) is analyzed. It is shown that the model exhibits a ferromagnetic transition in one and two dimensions, providing 02. The asymptotic form of the spin-spin correlation function (r) is studied in the neighborhood of the critical temperature T₂. At T=T₂, (r) decays for large r as 1{r^d-}. Several two-dimensional models with long-range interactions falling off as 1{r^2} in certain directions only are also investigated.
G S Joyce (Fri,) studied this question.
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