Optimal parallel acceleration of flat-histogram Monte Carlo sampling methods for atomistic simulation

Flat-histogram methods such as Wang–Landau sampling [1] enable efficient, high-throughput calculation of phase diagrams in atomistic and lattice-model systems. Several parallelisation schemes have been proposed to enhance sampling across distributed architectures [2–4]. Here, these schemes are systematically benchmarked—individually and in combination—to establish best practices for scalable flat-histogram simulations [5]. The strategies examined include energy-domain decomposition with static and dynamically sized sub-domains (the latter introduced here), replica exchange, and multiple random walkers per sub-domain. We assess how these factors affect parallel efficiency, load balance, and the role of sub-domain overlap. As a test case, we implement [6] and apply [7] these methods to a lattice model of the AlTiCrMo refractory high-entropy superalloy, which orders into a B2 (CsCl) phase with decreasing temperature. Results show superlinear speedup from energy-domain decomposition and that non-uniform energy sub-domains outperform adding random walkers.

[1] F. Wang, D.P. Landau, Phys. Rev. Lett. 86, 2050 (2001).

[2] T. Vogel et al., Phys. Rev. Lett. 110, 210603 (2013).

[3] J. Zierenberg et al., Comput. Phys. Commun. 184, 1155–1162 (2013).

[4] J. Gross et al., Comput. Phys. Commun. 229, 57–67 (2018).

[5] H.J. Naguszewski et al., arXiv:2510.11562.

[6] H.J. Naguszewski et al., arXiv:2505.05393.

[7] C.D. Woodgate, H.J. Naguszewski et al., J. Phys.: Mater. 8, 045002 (2025).