Does hard core interaction change absorbing-type critical phenomena?

Area of Science:

• Statistical Physics
• Complex Systems
• Nonlinear Dynamics

Background:

• Absorbing-type critical phenomena are typically studied assuming negligible hard core interactions due to low particle densities.
• The role of hard core interactions in these systems has been largely overlooked.

Purpose of the Study:

• To investigate the influence of hard core interactions on N-species branching annihilating random walks.
• To determine how these interactions modify absorbing-type critical phenomena.

Main Methods:

• Analytical predictions using a Langevin equation-type approach.
• Validation through direct numerical simulations.

Main Results:

• Hard core interactions were found to drastically alter absorbing-type critical phenomena in a nontrivial manner.
• Analytical predictions for scaling exponents (nu(perpendicular)=2, z=2, alpha=1/2, beta=2 in 1D for N>1) were confirmed by simulations.
• Varying diffusion coefficients led to continuous changes in nu(perpendicular) and beta.

Conclusions:

• Hard core interactions are crucial and not irrelevant to absorbing-type critical phenomena.
• The study provides a new understanding of phase transitions in systems with interacting particles.