II. Exact solutions of disordered Ising spin chains in a magnetic field

The one‐dimensional Ising model with arbitrary nearest neighbor interactions and a magnetic field is formulated in terms of the spin correlation function relations derived in the preceding article I. The local magnetization and the two‐spin correlation functions are shown to satisfy a set of coupled algebraic summation equations. The solution of this set is given in terms of a power series in hyberbolic tangents of the magnetic field strength, for chains of arbitrary length. For cases in which the interaction constants are random variables, explicit expressions are derived for the configurational averaged magnetization and the two‐spin correlation functions to the lowest order in the magnetic field.