Multidimensional mappings and lyapunov exponent of potts model with competing interactions

Abstract

The Potts model was introduced as a generalization of the Ising model to more than two components and was described as an easily defined class of statistical mechanics models. This study addresed the phase diagram of Potts model on a Cayley tree of arbitrary order with competing nearest-neighbour interactions , prolonged next-nearest-neighbour interactions and one-level next-nearest-neighbour interactions . Based on the Potts model on arbitrary order Cayley tree; a general system of equations was produced and the phase diagram was described. The phase diagram was investigated for several ranges of the competing parameters and it showed the appearance of several features and modulated phase arising from the frustration effects introduced by the one-level binary next-nearest-neighbour interaction. An iterative scheme similar to that appearing in real space renormalization group frameworks was established which recovers as particular case reported by Ganikhodjaev et. al. (2008) for . Furthermore, the variation of wavevector with temperature in the modulated phase was studied in detail where narrow commensurate steps between incommensurate regions appeared when investigating the Lyapunov exponent associated with trajectory of the system.