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, s_i= + 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^-2J_o/^k_B^T, 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, k_j(T), and corresponding free energies and interfacial tensions are derived explicitly for low temperatures.