Criticality in a model with absorbing states.

Area of Science:

• Statistical mechanics
• Complex systems

Background:

• Phase transitions are fundamental in physics.
• Understanding active-to-absorbing phase transitions is crucial for modeling various phenomena.

Purpose of the Study:

• To determine the critical point and critical exponents of a 1D active-to-absorbing phase transition model.
• To investigate the role of randomness in such transitions.

Main Methods:

• Monte Carlo simulations.
• Analytical arguments based on random-walk models.
• Analysis of reactivation probability.

Main Results:

• The exact critical point and critical exponents (delta=0.5, z=2) were predicted.
• Nonuniversal exponents (beta=nu(perpendicular)) were found to be linked to reactivation probability.
• A model with quenched randomness was also examined.

Conclusions:

• The study provides precise critical parameters for the investigated model.
• It highlights the nonuniversal nature of certain exponents and their connection to microscopic details.
• The findings offer insights into systems with quenched disorder.