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High resolution study of the two-dimensional axial next-nearest-neighbor Ising model using a two-replica cluster algorithm and population annealing
Phys. Rev. E 114, 044140 – Published 29 October, 2026
DOI: https://doi.org/10.1103/pvpn-49mz
Abstract
The axial next-nearest-neighbor Ising model in two dimensions is studied using population annealing combined with a two-replica cluster algorithm. We are able to fully resolve the sequence of sharp specific heat peaks that characterize the finite-size incommensurate floating phase. We also show that the two-replica cluster algorithm is much more effective in equilibrating the system than either single-replica cluster methods or the Metropolis algorithm when these are combined with population annealing. We argue that the effectiveness of the algorithm is due to its ability to move groups of defect lines between replicas combined with resampling in population annealing, which removes replicas from the population that have larger numbers of defect lines.
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