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

2003/03/13 by Paul Federbush, Federbush, Paul
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Random Matrices and Applications #Stochastic processes and statistical mechanics #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0303036

8 pages

arxiv created 2003/03/13 · arxiv updated 2009/11/30

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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