Low temperature analysis of the axial next-nearest neighbour Ising model near its multiphase point

Abstract

The general, axial next-nearest neighbour Ising (or ANNI) model inddimensions consists of (d— 1)-dimensional layers of spins, si= + 1, with nearest-neighbour ferromagnetic coupling, J0> 0, within layers but competing ferromagnetic, and antiferromagnetic,J2< 0, first- and second-neighbour axial coupling between layers. By systematic low temperature expansions in powers of e-2Jo/kBT, extended to all orders where necessary, it is shown ford> 2 that in the vicinity of amultiphasepoint atT= 0 and k = —J2/J1= 1/2 there occurs an infinite sequence of distinct, commensurate modulated phases characterized by wavevectors + l)< z for j = 0, 1, 2, .... The phase boundaries, kj(T), and corresponding free energies and interfacial tensions are derived explicitly for low temperatures.