Phase transitions in nonequilibrium d-dimensional models with q absorbing states

Area of Science:

• Statistical physics
• Complex systems modeling
• Phase transitions

Background:

• Nonequilibrium models are crucial for understanding systems far from equilibrium.
• The Potts model is a fundamental framework for studying phase transitions.
• Investigating variations of the Potts model provides insights into diverse physical phenomena.

Purpose of the Study:

• To investigate the phase transitions of a nonequilibrium Potts-like model with q absorbing states.
• To determine the nature of phase transitions in different dimensions (d) and numbers of absorbing states (q).
• To compare the model's phase diagram with that of the equilibrium Potts model.

Main Methods:

• Monte Carlo simulations were employed to study the model's behavior.
• Simulations were conducted in two (d=2) and three (d=3) dimensions.
• Analysis focused on identifying transition types (discontinuous or continuous) and critical exponents.

Main Results:

• In 2D with q=3, a discontinuous phase transition was observed.
• In 3D with q=2, a continuous phase transition with beta=1 (mean-field) was found.
• Simulations for 2D with q=2 were inconclusive, suggesting proximity to a multicritical point.

Conclusions:

• The model's phase diagram in the (q,d) plane resembles that of the equilibrium Potts model.
• The study confirms field-theory predictions regarding directed percolation universality for specific random walk models.
• The inconclusive results for 2D, q=2 indicate a complex region possibly at the intersection of different transition types.