Potts Model with Competing Interactions on a Cayley Tree of k-th Order

ISBN: 978-981-08-8407-9

Authors: Nasir Ganikhodjaev and Ashraf Mohamed Nawi

Abstract:

We study the phase diagram for Potts model on a Cayley tree of arbitrary order k with competing nearest-neighbor interactions J1, prolonged next-nearest-neighbor interactions Jp and one level k-tuple neighbors interaction J0. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers as particular case, previous works by Ganikhodjaev et al for k = 2. The phase diagram is studied for several ranges of the competing parameters showing the appearance of several features and modulated phase arising from the frustration effects introduced by the one-level k-tuple neighbor interaction J0.

Keywords: componets - Potts model; Cayley tree; phase diagram; one-level next-nearest-neighbour; modulated phase; average magnetization