Strange attractors in the vannimenus model on an arbitrary order cayley tree

Abstract

We consider the Vannimenus model on a Cayley tree of arbitrary order k with competing nearest-neighbour interactions J1 and next-nearest- neighbour interactions J2 and J3 in the presence of an external magnetic field h. In this paper we study the phase diagram of the model using an iterative scheme for a renormalized effective nearest-neighbour coupling Kr and effective field per site Xr for spins on the rth level; it recovers, as particular cases, previous works by Vannimenus, Inawashiro et al, Mariz et al and Ganikhodjaev and Uuz. Each phase is characterized by a particular attractor and the phase diagram is obtained by following the evolution and detecting the qualitative changements of these attractors. These changements can be either continuous or abrupt, respectively characterizing second- or first- order phase transitions. We present a few typical attractors and at finite temperatures, several interesting features (evolution of reentrances, separation of the modulated region into few disconnected pieces, etc) are exhibited for typical values of parameters. © Published under licence by IOP Publishing Ltd.