Probability distribution of the order parameter in the directed percolation universality class

Area of Science:

• Statistical Physics
• Complex Systems

Background:

• Directed percolation universality class models are crucial for understanding critical phenomena.
• Analyzing nonequilibrium phase transitions often requires specialized techniques.

Purpose of the Study:

• To evaluate order parameter probability distributions for two models within the directed percolation universality class.
• To demonstrate the utility of probability distribution functions in identifying critical points for nonequilibrium systems.

Main Methods:

• Monte Carlo simulations were conducted for the one-dimensional generalized contact process and the Domany-Kinzel cellular automaton.
• The density of active sites was utilized as the order parameter.

Main Results:

• Criticality was determined solely through the analysis of the order parameter's probability distribution function.
• The method proved effective in identifying critical points for both simulated models.

Conclusions:

• The probability distribution function method is a viable approach for studying nonequilibrium phase transitions.
• This technique extends successfully from equilibrium systems to nonequilibrium phenomena, offering a unified analytical framework.