Monte Carlo study of the spatially modulated phase in an Ising model

Abstract

The spatially modulated or "sinusoidal" phase which occurs in a three-dimensional spin-½ Ising model with competing ferromagnetic and antiferromagnetic interactions between adjacent and next-nearest $\mathrm{xy}$ layers is studied by Monte Carlo methods. The equilibrium wave vector, $q\left(T\right)\mathrm{}$, changes, possibly with jumps, from $q=\frac{\pi }{2a}$ at $T=0\mathrm{}$, to its near-critical value: for $-\frac{J_2}{J_1}=0.6\mathrm{}$, the change occurs rapidly in the interval $0.8 T_c$ to $0.9 T_c$. The magnetization wave form appears to display distinct, although small, third harmonic components up to $T_c$.