Potts model with competing interactions on Kth order Cayley tree

Abstract

We study the phase diagram of Potts model on a Cayley tree of arbitrary order K with competing nearest-neighbour interactions J1, prolonged next-nearest-neighbour interactions Jp and one-level K-tuple neighbours interaction J0. Towards implement this study, an iterative structure similar to that appearing in real space renormalization group frameworks is established; it expands as particular case, and finds the new modulated phases in addition to the expected paramagnetic, ferromagnetic and antiferromagnetic phases. The phase diagram is considered for some varieties of the competing parameters showing the form of several structures and modulated phase arising from the frustration effects introduced by the one-level K-tuple neighbour interaction J0. The variant of the wavevector with temperature in the modulated phase is calculated in detail; it shows narrow proportionate steps among disproportionate regions. Finally, this thesis anticipates the explanation of the behaviour inside the modulated phase with providing several study results.