For the Quantum Heisenberg Ferromagnet, a Polymer Expansion and its High T Convergence

2001/08/02 by Paul Federbush, Federbush, Paul
Mathematics · Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #Mathematical Physics (math-ph) #cond-mat #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0108002

LaTeX, 35 pages

arxiv created 2001/08/02 · arxiv updated 2009/11/30

Abstract

We let Psi₀ be a wave function for the Quantum Heisenberg ferromagnet sharp i sigma_zi and Psi_mu = exp(-mu*H)Psi₀. 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 wavefunction 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)), where phi satisfies 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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