Numerical study of persistence in models with absorbing states

Area of Science:

• Statistical Physics
• Complex Systems
• Computational Physics

Background:

• The Ziff-Gulari-Barshad (ZGB) model is a fundamental framework for studying irreversible reaction dynamics.
• Understanding persistence exponents is crucial for characterizing the long-term behavior of systems near phase transitions.
• Previous studies have explored various aspects of the ZGB model, but detailed analysis of local and global persistence at different phase transition orders is ongoing.

Purpose of the Study:

• To evaluate local and global persistence exponents in the Ziff-Gulari-Barshad (ZGB) irreversible reaction model.
• To investigate the behavior of persistence at both second-order and first-order irreversible phase transitions (IPTs).
• To explore universality issues by comparing persistence in the ZGB model with the contact process in various dimensions.

Main Methods:

• Extensive Monte Carlo simulations were employed to model the ZGB irreversible reaction process.
• Local (theta(l)) and global (theta(g)) persistence exponents were calculated.
• The contact process, another model with absorbing states, was studied in dimensions 1 to 4 to analyze universality.

Main Results:

• At the second-order IPT, both local and global persistence exhibit power-law behavior with a two-regime crossover.
• At the ZGB first-order IPT, persistence decays abruptly, and power-law behavior is uncertain.
• Apparent superuniversality was observed, with the local persistence exponent appearing to be the same in one- and two-dimensional contact processes.

Conclusions:

• The ZGB model displays distinct persistence behaviors at different orders of phase transitions.
• The findings suggest potential universality across different models and dimensions for local persistence.
• Further analysis of persistence in systems with absorbing states is warranted.