Ground state phase diagrams of spin [formula omitted] extended ANNNI and BNNNI models

Abstract

By using the fundamental spin arrangement (FSA) method, the ground state phase diagrams are determined exactly for one- (and, in some special cases, greater than one) dimensional spin S = 3 2 axial next nearest-neighbour Ising (ANNNI) models. For the ordinary ANNNI model having only bilinear exchange interactions, the phase diagram agrees, apart from a simple scaling, with those of the S = 1 2 and S = 1 systems, supporting the conjecture that to this extent it does not depend on the spin quantum number S. Extended ANNNI models having higher order exchange interactions exhibit far richer phase diagrams with various modulated ferromagnetic and antiferromagnetic phases represented by FSA up to six spins in length. The phase diagrams obtained here also hold for the biaxial next nearest-neighbour Ising (BNNNI) model in which nearest and next-nearest neighbour interactions compete with each other in each of two directions.