Ising Model on a General Cayley Tree with Competing Next-nearest-neighbour Interactions

ISBN: 978-981-08-8407-9

Authors: Nasir Fanikhodjaev and Siti Fatimah Zakaria

Abstract:

We study the Ising model on a general Cayley tree of arbitrary order and produce the phase diagram with competing interactions prolonged next-nearest-neighbour Jp and one-level k-tuple next-nearest-neighbour Jo. Vannimenus proved the existence of modulated phase in the phase diagram of Ising model with competing nearest-neighbour interaction J1 and prolonged next-nearest-neighbour interactions Jp, as found for similar models on periodic lattices.

Keywords: Ising model, Cayley tree, prolonged next-nearest-neighbour, one-level next-nearest-neighbour.