Critical phenomena in the majority voter model on two-dimensional regular lattices

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• Understanding critical phenomena is crucial in statistical mechanics.
• Lattice models provide a framework for studying phase transitions.
• The Ising model is a fundamental model for ferromagnetism and critical behavior.

Purpose of the Study:

• To investigate the critical behavior of the critical point.
• To analyze the influence of nearest neighbors on critical points.
• To compare critical points across different 2D regular lattices.

Main Methods:

• Numerical simulations were conducted on triangular, hexagonal, and bilayer square lattices.
• Finite-size scaling theory was applied to analyze simulation data.
• Critical point values were determined for each lattice type.

Main Results:

• All simulated lattices, except the bilayer square lattice, belong to the 2D Ising model universality class.
• The critical point value for the bilayer square lattice deviates from the expected trend.
• This deviation suggests unique critical behavior in the bilayer system.

Conclusions:

• The number of nearest neighbors significantly impacts critical point behavior.
• Bilayer square lattices exhibit distinct critical properties not captured by the standard 2D Ising model.
• Further research is needed to elucidate the behavior of bilayer systems.