Phase transitions in a simple growth model for a driven interface in random media

Area of Science:

• Physics
• Statistical Mechanics
• Complex Systems

Background:

• Driven interfaces in random media are crucial for understanding phenomena like crystal growth and fracture.
• Nonequilibrium systems exhibit complex phase transitions not found in equilibrium systems.
• Universality classes describe the collective behavior of diverse systems near critical points.

Purpose of the Study:

• To introduce and analyze a novel (1+1)-dimensional growth model for driven interfaces in random media.
• To investigate the nature of smoothing (roughening) and pinning-depinning transitions within this model.
• To determine the universality classes associated with these critical phenomena.

Main Methods:

• Development of a simple growth model for a driven interface in random media.
• Analysis of scaling exponents at transition points.
• Classification of transitions based on universality classes, including directed percolation and quenched Kardar-Parisi-Zhang.

Main Results:

• The model exhibits both smoothing (roughening) and pinning-depinning transitions.
• At both transition points, scaling exponents align with the directed percolation universality class.
• The rough interface at the pinning-depinning transition belongs to the quenched Kardar-Parisi-Zhang universality class.
• Both transitions are identified as second-order phase transitions.
• A modified model demonstrates a first-order pinning-depinning transition within the directed percolation universality class.

Conclusions:

• The introduced growth model provides a framework for studying critical phenomena in driven interfacial systems.
• The findings highlight the role of the directed percolation universality class in (1+1)-dimensional nonequilibrium systems.
• The study distinguishes between second-order and first-order phase transitions in related interfacial models.