Two-dimensional Potts model with invisible states on a square lattice

Area of Science:

• Statistical mechanics
• Condensed matter physics
• Computational physics

Background:

• The ferromagnetic Potts model is a fundamental model in statistical mechanics.
• Understanding phase transitions in systems with both interacting and noninteracting components is crucial.
• Investigating the influence of invisible states on model behavior provides new insights.

Purpose of the Study:

• To investigate the phase transitions in a two-dimensional (q+r)-state ferromagnetic Potts model.
• To determine the critical value (r_c) separating second-order and first-order phase transitions for q=2.
• To elucidate the underlying mechanism of the first-order phase transition.

Main Methods:

• Utilizing the Wang-Landau Monte Carlo simulation method to calculate the density of states.
• Employing the Metropolis algorithm to compute the density of visible spins.
• Analyzing specific heat, partition function zeros, and internal energy probability distributions.

Main Results:

• A second-order phase transition occurs for r < r_c, and a first-order transition for r > r_c.
• The critical value r_c is determined to be approximately 29 for q=2.
• The first-order phase transition is attributed to an abrupt change in the density of visible spins.

Conclusions:

• The number of noninteracting invisible states significantly alters the nature of phase transitions in the ferromagnetic Potts model.
• The critical value r_c ≈ 29 marks a distinct shift in system behavior.
• The density of visible spins is a key factor driving the first-order phase transition.