Periodic structure of the effective fields for a regular Ising model on the Cayley tree at T=0

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Abstract
The regular Ising model with l bonds of J>0 and l bonds of -J on the Cayley tree with coordination number 2l is considered under the uniform external field when l>or=3. The effective fields in the system satisfy nonlinear coupled recursive equations. At T=0, these become piecewise linear equations and arithmetic furcations of periodic points for the recursive equations are found as a function of the external field.