An infinity of commensurate phases in a simple Ising system: The ANNNI model (invited)

Publisher Website
Google Scholar
Abstract
The ANNNI or axial next‐nearest neighbor Ising model in d dimensions consists of (d−1)‐dimensional layers of Ising spins, si = ±1, with nearest neighbor ferromagnetic couplings, J0≳0, within layers but competing ferromagnetic, J1, and antiferromagnetic, J2 = −κJ1model expected to display spatially modulated magnetically ordered states with wavevectors nontrivially related to the lattice spacing a, as observed in various real systems. The ground state is ferromagnetic for κground states and carried to all orders where necessary. For d≳2 they show that (T,κ) = (0,1/2) is a multiphase point from which spring an infinite sequence of distinct, spatially modulated commensurate phases, 〈2j−13〉, with wavevectors q̄ = πj/(2j+1)a for j = 1,2, ⋅⋅⋅ . The free energy, phase boundaries, and corresponding domain wall energies can be given explicitly at low temperatures. On approaching the ’’melting’’ line, κ∞(T), of the 〈2〉 phase the wavevector varies quasicontinuously as 1/‖1n[κ∞(T)−κ]‖, displaying a ’’devil’s top step’’ just as the 〈2〉 phase locks in.