Paul Federbush Single Site Spin Expectation for the Imaginary Time Heisenberg Ferromagnet Wave Function, Numerical Approximation and Theoretical Argument (12K, LaTeX) 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.