INTERACTING-WALLS APPROXIMATION IN THE 2-DIMENSIONAL AXIAL 3RD-NEAREST-NEIGHBOR ISING-MODEL

The two-dimensional axial Ising model with competing interactions up to third neighbors is studied by analytical methods. A low-temperature approximation is used to describe the system as a sequence of interacting and nonreversing domain walls for small values of the third-neighbor interaction. The boundaries of the ferromagnetic and other low-temperature modulated phases are obtained by means of the ground-state energy of the Heisenberg-Ising chain after reducing the problem to a system of spinless interacting fermions in one dimension. The density of walls or wave number obtained within this approximation results to be continuously varying and for some relations among the coupling constants it displays plateaus and re-entrant phenomena. © 1990 The American Physical Society.