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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-Schrodinger expansion of the ground state eigenvector of a differential operator. The operator describes a Markovian time evolution of the ferromagnet.

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