Absorbing state phase transitions with quenched disorder

Area of Science:

• Statistical Physics
• Complex Systems
• Phase Transitions

Background:

• Quenched disorder is a relevant perturbation at absorbing state phase transitions.
• Understanding its impact is crucial for characterizing critical phenomena.

Purpose of the Study:

• Investigate the properties of random fixed points in systems with quenched disorder.
• Analyze the critical behavior of systems within the directed percolation universality class under strong disorder.

Main Methods:

• Employed a strong disorder renormalization group framework.
• Utilized effective numerical methods for analysis.
• Studied the random contact process in one and two dimensions.

Main Results:

• Identified a strong disorder fixed point controlling critical behavior for strong disorder, isomorphous with random quantum Ising systems.
• Observed logarithmically slow dynamical correlations and conjectured exact static critical exponents for 1D systems.
• Found numerical evidence for disorder-dependent static critical exponents and two scenarios for dynamical correlations under weaker disorder.

Conclusions:

• The strong disorder fixed point governs critical behavior in certain systems.
• Numerical results align with the renormalization group predictions for the random contact process.
• Further investigation is needed to fully resolve the behavior under weaker disorder.