Single Site Spin Expectation for the Imaginary Time Heisenberg Ferromagnet Wave Function, Numerical Approximation and Theoretical Argument

TL;DR

This paper investigates approximations of spin expectations in the imaginary time Heisenberg ferromagnet, combining numerical, theoretical, and probabilistic methods to validate a key randomness assumption.

Contribution

It introduces a novel approximation method based on the lattice heat equation and provides a theoretical argument supporting a crucial randomness assumption.

Findings

Numerical results support the approximation accuracy.

Theoretical analysis suggests the randomness assumption is likely correct.

The approach bridges numerical, theoretical, and probabilistic perspectives.

Abstract

Certain approximations for the spin expectations have been studied both numerically and theoretically. Approximations are constructed using solutions of the lattice heat equation. The most interesting idea is a certain randomness assumption for a theoretically derived quantity, that leads directly to a given approximation. We are betting the randomness assumption is rigorously correct.