A Polymer Expansion for the Quantum Heisenberg Ferromagnet Wave Function

TL;DR

This paper introduces a polymer expansion for the quantum Heisenberg ferromagnet wave function on finite lattices, emphasizing algebraic identities and suggesting that large polymers have minimal effects, with potential extensions to infinite systems.

Contribution

It presents a novel algebraic polymer expansion for the quantum Heisenberg ferromagnet wave function, highlighting its simplicity and potential for extension to infinite lattices.

Findings

Polymer expansion is algebraically elegant and simple.

Large polymers are conjectured to have small effects.

Expansion may be extended to infinite volume systems.

Abstract

A polymer expansion is given for the Quantum Heisenberg Ferromagnet wave function. Working on a finite lattice, one is dealing entirely with algebraic identities; there is no question of convergence. The conjecture to be pursued in further work is that effects of large polymers are small. This is relevant to the question of the utility of the expansion and its possible extension to the infinite volume. In themselves the constructions of the present paper are neat and elegant and have surprising simplicity.