The Ising model on the Bethe lattice of general connectivity, with competing interactions between the first-, second-, and third-neighbor spin generations has been studied. In our approach the partition function, the local magnetization and the pair correlation function are obtained exactly by solving a set of coupled recursion relations of appropriated effective fields. The phase diagram is studied for several ranges of the competing parameters showing the appearance of several features and modulated phases arising from the frustration effects introduced by the third-nearest-neighbor interaction. The ground-state phase diagram is obtained analytically by a minimization procedure and the infinite-connectivity limit is worked out, recovering previous results.

• Received 11 August 1986

DOI:https://doi.org/10.1103/PhysRevB.34.7975