  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.
