Population Annealing with Two-Replica Cluster Moves for the ANNNI Model

We explore a simulation method for the axial next-nearest neighbor Ising (ANNNI) model, which includes nearest-neighbor ferromagnetic couplings in all directions and next-nearest-neighbor antiferromagnetic couplings in the z-direction, determined by a tunable coupling-ratio. We use a Monte Carlo simulation method that combines two-replica cluster moves and population annealing. The efficiency of the two-replica cluster method for the 2D ANNNI model is compared to the Wolff cluster algorithm as modified for frustrated systems by Pleimling and Henkel. Our approach is significantly more efficient when the antiferromagnetic coupling dominates, and enables effective equilibrium simulations of relatively large lattices in this regime. We compare our results for the incommensurate floating phase with those in the literature. Finally, we discuss reasons for the efficiency of two-replica cluster moves combined with population annealing for the ANNNI model and, potentially, other spin systems with structured frustration.