Paul Federbush
A Polymer Expansion for the Random Walk on the
Permutation Group Associated to the Quantum
Heisenberg Ferromagnet
(15K, LaTeX)
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.