We present a mechanism for displaying the transmission property of the discrete Heisenberg ferromagnetic (DHF) spin chain via a geometric approach. With the aid of a discrete nonlinear Schrödinger-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 nontransmitting behavior for the DHF, with a large probability, is revealed by an adoption of various stochastic algorithms.

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