Phase diagram of a square Ising model with exchange and dipole interactions: Monte Carlo simulations

Abstract

The thermal behavior of the square Ising model with exchange $(J)$ and dipole $(g)$ interactions is well understood for values of $J∕g$ far from the phase boundaries between striped configurations of different widths $h$. A variety of phase transitions were found by Monte Carlo simulations. Both first order and continuous phase transitions were found depending on the value of the ratio $J∕g$, but no intermediate phase was found between the low temperature ordered striped phase and the high temperature paramagnetic one. Here, we investigate the regions of $J∕g$ near the boundaries between the striped phases of width $h$ and $h+1$. We find that for $h=2,3$, an intermediate (modulated) phase occurs between the striped and paramagnetic phases. Of particular interest is the region around the boundary between the N\'eel phase and the striped phase with $h=1$ where an infinite sequence of $⟨1,n⟩$ $(⟨n,1⟩)$ configurations, never seen before, are found to become stable. They are characterized by horizontal (vertical) stripes made up of $n$ identical antiferromagnetic rows (columns) alternated with $n$ antiferromagnetic rows (columns) of spins reversed. The accumulation point of this sequence $(n\ensuremath{\rightarrow}\ensuremath{\infty})$ corresponds to the striped phase with $h=1$ (columnar phase).