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Transactions of the American Mathematical Society

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


Author: William G. Faris
Journal: Trans. Amer. Math. Soc. 261 (1980), 579-587
MSC: Primary 82A05; Secondary 47A55, 60K35
DOI: https://doi.org/10.1090/S0002-9947-1980-0580904-1
MathSciNet review: 580904
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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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DOI: https://doi.org/10.1090/S0002-9947-1980-0580904-1
Keywords: Heisenberg ferromagnet, diffusion in infinite dimensions, Gibbs state, Kirkwood-Salsburg equations, high temperature expansion
Article copyright: © Copyright 1980 American Mathematical Society

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