Strong disorder fixed point in absorbing-state phase transitions.

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Complex systems

Background:

• Nonequilibrium phase transitions are crucial in understanding dynamic systems.
• Directed percolation describes a wide range of phenomena, from forest fires to epidemics.
• The influence of quenched disorder on these transitions is a key theoretical challenge.

Purpose of the Study:

• To investigate the effect of quenched disorder on critical behavior within the directed percolation universality class.
• To determine if a strong disorder fixed point governs the system's behavior.
• To calculate critical exponents and analyze their dependence on disorder strength.

Main Methods:

• Utilizing a strong disorder renormalization group approach.
• Performing density matrix renormalization group calculations.
• Analyzing critical behavior in one and two dimensions.

Main Results:

• For strong quenched disorder, critical behavior is governed by a stable strong disorder fixed point.
• In one dimension, exact critical exponents beta=(3-sqrt[5])/2 and nu(perpendicular)=2 are conjectured.
• Disorder-dependent critical exponents emerge outside the fixed point's attractive region, with similar scenarios applicable to two dimensions.

Conclusions:

• Quenched disorder fundamentally alters critical phenomena in directed percolation.
• The identified strong disorder fixed point provides a new framework for understanding these systems.
• The findings offer a unified interpretation for existing numerical results in both one and two dimensions.