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

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.

8 pages

References in corpus (4)

• For the Quantum Heisenberg Ferromagnet, Some Conjectured Approximations
• A Polymer Expansion for the Quantum Heisenberg Ferromagnet Wave Function
• For the Quantum Heisenberg Ferromagnet, Tao to the Proof of a Phase Transition
• For the Quantum Heisenberg Ferromagnet, a Polymer Expansion and its High T Convergence