paul federbush
For the Quantum Heisenberg Ferromagnet, a Polymer Expansion and its 
High T Convergence
(52K, LaTeX)

ABSTRACT.   We let Psi_0 be a wave function for the Quantum Heisenberg Ferromagnet 
sharp in the sigma_zi and Psi_mu = exp(-mu*H)Psi_0. We study expectations 
similar to the form 
 <Psi_mu,(sigma_zi)Psi_mu>/<Psi_mu,Psi_mu> 
for which we present a formal polymer expansion, whose convergence we 
prove for sufficiently small mu. 
 The approach of the paper is to relate the wave function Psi_mu 
to an approximation to it that is a product function. In the jth spot 
of the product approximation the upper component is phi_mu(j), and 
the lower component is (1-phi_mu(j)). The phi is a solution of the 
lattice heat equation. This is shown via a cluster or polymer 
expansion. 
 The present work began in a previous paper, primarily a numerical 
study, and provides a proof of results related to Conjecture 3 of 
this previous paper.