The Transmission Property of the Discrete Heisenberg Ferromagnetic Spin Chain

TL;DR

This paper investigates the transmission properties of the discrete Heisenberg ferromagnetic spin chain using a geometric approach, revealing bistability in transmission coefficients and a new invariant periodic phenomenon in non-transmitting behavior.

Contribution

It introduces a geometric method to analyze transmission in the DHF, showing bistability and discovering a novel invariant periodic phenomenon in non-transmitting states.

Findings

Transmission coefficients are bistable.

A new invariant periodic phenomenon in non-transmitting behavior.

Stochastic algorithms effectively reveal transmission properties.

Abstract

We present a mechanism for displaying the transmission property of the discrete Heisenberg ferromagnetic spin chain (DHF) via a geometric approach. By the aid of a discrete nonlinear Schr\"odinger-like equation which is the discrete gauge equivalent to the DHF, we show that the determination of transmitting coefficients in the transmission problem is always bistable. Thus a definite algorithm and general stochastic algorithms are presented. A new invariant periodic phenomenon of the non-transmitting behavior for the DHF, with a large probability, is revealed by an adoption of various stochastic algorithms.