Topology of feedback in the theory of molecular field

Diagrammatic technique is used to represent causal structure of the Weiss theory of inner molecular field in ferromagnetism. The diagram, consisting of vertices H (applied magnetic field), Hloc (local field), Hi (interaction field) and M (magnetization) contains a closed path—feedback loop—that is shown to control the hysteresis phenomena. In particular, a sigmoidal M–H characteristic occurs if and only if the so-called transmission function of this loop crosses the critical level of unity at two distinct states. The formalism of transmission functions yields a differential equation of the M–H characteristics and a routine for evaluating implicit dependences. Results of numerical study are presented to demonstrate the approach.