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A Polymer Expansion for the Random Walk on the Permutation Group Associated to the Quantum Heisenberg Ferromagnet

Paul Federbush
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Abstract

For a long time one has associated to the Quantum Heisenberg Ferromagnet on a lattice, a random walk on the permutation group of the lattice vertices. We here present a polymer expansion for the solution of the heat equation coupled to the random walk. We work on a finite lattice, there is no question of convergence. We leave to future work bounding terms in the expansion necessary to extend the result to an infinite lattice.

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Paul Federbush. 2003-03-13. A Polymer Expansion for the Random Walk on the Permutation Group Associated to the Quantum Heisenberg Ferromagnet. https://arxiv.org/abs/math-ph/0303036

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