LYAPUNOV EXPONENTS AND MODULATED PHASES OF AN ISING MODEL ON CAYLEY TREE OF ARBITRARY ORDER

Different types of the lattice spin systems with the competing interactions have rich and interesting phase diagrams. In this study a system with competing nearest-neighbor interaction J(1), prolonged next-nearest-neighbor interaction J(p) and ternary prolonged interaction J(tp) is considered on a Cayley tree of arbitrary order k. To perform this study, an iterative scheme is developed for the corresponding Hamiltonian model. At finite temperatures several interesting properties are presented for typical values of alpha T/J(1), beta = -J(p)/J(1) and gamma = -J(tp)/J(1). This study recovers as particular cases, previous work by Vannimenus(1) with gamma = 0 for k = 2 and Ganikhodjaev et al.(2) in the presence J(1), J(p), J(tp) with k = 2. The variation of the wavevector q with temperature in the modulated phase and the Lyapunov exponent associated with the trajectory of our iterative system are studied in detail.