Competing binary and k-tuple interactions on a Cayley tree of arbitrary order

We study the phase diagram for the Ising model on a Cayley tree of arbitrary order k with competing nearest-neighbor interactions J(1), prolonged next-nearest-neighbor interactions J(p), and one-level k-tuple neighbor interaction J(o). The phase diagram is studied for several ranges of the competing parameters; it shows the appearance of several features and modulated phases arising from the frustration effects introduced by the one-level k-tuple neighbor interaction J(o). The variation of the wayevector with temperature in the modulate phase is studied in detail; it shows narrow commensurate steps between incommensurate regions. Finally, the Lyapunov exponent associated with the trajectory of the system is investigated. (C) 2011 Elsevier B.V. All rights reserved.