Contact process in disordered and periodic binary two-dimensional lattices.

Area of Science:

• Statistical Physics
• Complex Systems
• Computational Physics

Background:

• The contact process (CP) is a fundamental model for epidemic spread and population dynamics.
• Understanding critical phenomena in disordered systems is crucial for realistic modeling.
• Previous studies suggested unique behavior for the 2D disordered CP.

Purpose of the Study:

• To numerically and analytically investigate the critical behavior of the 2D contact process in disordered and periodic lattices.
• To determine how disorder strength affects static and dynamic scaling exponents.
• To verify the universality class of the disordered 2D CP.

Main Methods:

• Monte Carlo simulations were employed for numerical investigations.
• Quasistationary simulations were used to obtain static scaling exponents.
• Analytical approximation and standard mean field theory were applied.
• Finite-size scaling analysis was performed.

Main Results:

• Numerical phase-separation lines closely matched analytical predictions.
• Static scaling exponents in disordered lattices varied with disorder strength.
• The finite-size scaling exponent approached a value indicative of an infinite-randomness fixed point.
• Both dynamical and static scaling exponents converged to values from the homogeneous case.

Conclusions:

• The 2D disordered contact process belongs to the directed percolation universality class.
• Disorder influences critical behavior, potentially leading to an infinite-randomness fixed point.
• The findings confirm the robustness of the directed percolation universality class in heterogeneous environments.