 01295 paul federbush
 For the Quantum Heisenberg Ferromagnet, a Polymer Expansion and its
High T Convergence
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Aug 2, 01

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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 (1phi_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.
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