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  • Open Access

Cluster percolation and dynamical scaling in the Baxter-Wu model

Alexandros Vasilopoulos1,*, Michail Akritidis2,†, Nikolaos G. Fytas1,‡, and Martin Weigel3,4,§

  • *Contact author: alex.vasilopoulos@essex.ac.uk
  • †Contact author: michalis.akritidis@u-bourgogne.fr
  • ‡Contact author: nikolaos.fytas@essex.ac.uk
  • §Contact author: martin.weigel@physik.tu-chemnitz.de
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Phys. Rev. E 113, 014129 – Published 22 January, 2026

DOI: https://doi.org/10.1103/9425-hxtb

Abstract

We investigate the percolation behavior of Fortuin-Kasteleyn-type clusters in the spin-1/2 Baxter-Wu model with three-spin interactions on a triangular lattice. The considered clusters are constructed by randomly freezing one of the three sublattices, resulting in effective pairwise interactions among the remaining spins. Using Monte Carlo simulations combined with a finite-size scaling analysis, we determine the percolation temperature of these stochastic clusters and show that it coincides with the exact thermal critical point of the model. The critical exponents derived from cluster observables are consistent with those of the underlying thermal phase transition. Finally, we analyze the dynamical scaling of the multicluster and single-cluster algorithms resulting from the cluster construction, highlighting their efficiency and scaling behavior with system size.

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Phys. Rev. E 113, 014129– Published 22 January, 2026
  • Received 21 October 2025
  • Accepted 5 January 2026
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