  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.
