Potts and percolation models on bowtie lattices.

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• The Potts model is a fundamental model in statistical mechanics.
• Understanding critical phenomena and phase transitions is crucial in physics.
• Bowtie lattices present unique geometric properties influencing physical models.

Purpose of the Study:

• To determine the exact critical frontier of the Potts model on bowtie lattices.
• To validate theoretical predictions with extensive Monte Carlo simulations.
• To investigate percolation thresholds and shape-dependent properties on anisotropic lattices.

Main Methods:

• Exact analytical solutions for the Potts model critical frontier.
• Monte Carlo simulations for noninteger q Potts model.
• Simulation of bond and site percolation on bowtie lattices.

Main Results:

• The critical frontier for q=1 matches bond percolation thresholds.
• The q=2 critical point aligns with the Ising model on the bowtie lattice.
• Numerical results for noninteger q are accurate to seven significant digits and consistent with theory.
• Site percolation threshold determined as s(c) = 0.5479148(7).
• Shape-dependent properties differ from isotropic lattices due to anisotropy.

Conclusions:

• The study provides exact critical frontiers for the Potts model on bowtie lattices.
• Simulations validate theoretical findings and offer precise percolation thresholds.
• Lattice anisotropy significantly influences shape-dependent properties in percolation models.