Phase transitions in two-dimensional Potts models in an external field.

Area of Science:

• Statistical mechanics
• Condensed matter physics

Background:

• The q-state Potts model is a fundamental model in statistical mechanics.
• Understanding its phase transitions in external fields is crucial for condensed matter physics.

Purpose of the Study:

• To investigate the phase diagram of the q-state Potts model on a square lattice under an external magnetic field.
• To determine the nature of phase transitions and critical behavior for varying q values.

Main Methods:

• Extensive Monte Carlo simulations employing a hybrid algorithm (Metropolis with Wolff cluster updates).
• Single-histogram reweighting and field-mixing techniques for probability distributions.
• Finite-size scaling analysis of order parameters and distributions.

Main Results:

• A first-order transition line exists for positive fields, ending at a critical point in the 2D Ising universality class.
• The critical field vanishes as q approaches 5 from above (q→5⁺).
• For negative fields, a first-order transition line occurs for q≥6, with q=5 exhibiting a second-order transition line.

Conclusions:

• The q-state Potts model exhibits complex phase behavior dependent on the number of states (q) and magnetic field orientation.
• The universality class of transitions changes with q, particularly at q=5 and for negative fields.