Cluster percolation and dynamical scaling in the Baxter-Wu model.

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• The spin-1/2 Baxter-Wu model on a triangular lattice exhibits complex phase transitions.
• Fortuin-Kasteleyn-type clusters are crucial for understanding critical phenomena in statistical mechanics.
• Investigating percolation phenomena can reveal insights into underlying thermal phase transitions.

Purpose of the Study:

• To analyze the percolation behavior of Fortuin-Kasteleyn-type clusters in the spin-1/2 Baxter-Wu model.
• To determine the percolation temperature of stochastic clusters formed by sublattice freezing.
• To compare the critical exponents of cluster observables with the thermal phase transition exponents.

Main Methods:

• Monte Carlo simulations were employed to model the system.
• Finite-size scaling analysis was used to determine critical properties.
• Cluster construction involved randomly freezing one of the three sublattices.

Main Results:

• The percolation temperature of the stochastic clusters was found to coincide with the exact thermal critical point.
• Critical exponents derived from cluster observables matched those of the thermal phase transition.
• The dynamical scaling of multicluster and single-cluster algorithms was analyzed.

Conclusions:

• Percolation analysis of Fortuin-Kasteleyn-type clusters provides an accurate method for locating the thermal critical point.
• The study validates the consistency between percolation critical exponents and thermal phase transition exponents.
• The investigated cluster algorithms demonstrate efficient scaling behavior for large system sizes.