Journal of Statistical Physics, Vol. 35, Nos. 3/4, 1984, p. 355-374.
A regular Ising model with nearest-neighbor interactions of J and -J (J > 0) on a Cayley tree of coordination number 3 is investigated for the behavior of effective fields in a uniform external field. The effective fields show periodic and also aperiodic structures in the temperature-field plane. At absolute zero temperature, the equations determining effective fields are reduced to a nonlinear, one-dimensional, iterative equation. Arithmetic furcations of period and a "screening" of the furcations are observed.