The authors introduce a modified version of the Rose-Machta microcanonical population annealing algorithm to study the two-dimensional Blume-Capel model. The key idea is to use both an energy ceiling and an energy floor to cover the entire energy spectrum and obtain a good estimate of the density of states.
The algorithm is validated by comparing the results for the two-dimensional Ising model with the exact solution. The authors then apply the algorithm to the Blume-Capel model and analyze the finite-size scaling of the specific heat and Binder cumulant to study the evolution from the second-order Ising-like behavior through the tricritical point to the first-order behavior.
The results are in good agreement with previous numerical analyses using various methods, such as Monte Carlo, Wang-Landau, transfer-matrix, and series expansion. The authors observe a strong crossover effect near the first-order transition line, which requires more intensive analysis. The microcanonical population annealing algorithm is shown to be well-suited for massively parallel simulations and provides an efficient approach for modeling critical phenomena.
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arxiv.org
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