The Rayleigh-Schrödinger expansion of the Gibbs state of a classical Heisenberg ferromagnet

Faris, William G.

doi:10.1090/S0002-9947-1980-0580904-1

The Rayleigh-Schrödinger expansion of the Gibbs state of a classical Heisenberg ferromagnet
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by William G. Faris

Trans. Amer. Math. Soc. 261 (1980), 579-587

DOI: https://doi.org/10.1090/S0002-9947-1980-0580904-1

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Abstract:

The equilibrium Gibbs state of a classical Heisenberg ferromagnet is a probability measure on an infinite product of spheres. The Kirkwood-Salsburg equations may be iterated to produce a convergent high temperature expansion of this measure about a product measure. Here we show that this expansion may also be obtained as the Rayleigh-Schrödinger expansion of the ground state eigenvector of a differential operator. The operator describes a Markovian time evolution of the ferromagnet.

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