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1952
Spherical model of a ferromagnet
Let the spin values of the Ising ferromagnet take on
continuous values, and the partition function becomes a
tractable integral. Berlin and Kac constrained the sum of
the squares of the spin values to be equal to the number of
lattice sites, and obtained an exactly soluble three-
dimensional model that exhibited a phase transition in non-
zero field. The model did not approximate any known
physical systems, but it did later prove useful as a first
step in Wilson's application of the renormalization group.
Primary:
T. H. Berlin and M. Kac, "The spherical model of a
ferromagnet," Phys. Rev. 86 (1952): 821-835.
Secondary:
Domb 1996, 179.
Hoddeson et al. 1992, 574.
--Karl Hall
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