Critical behavior of the two-dimensional randomly driven lattice gas

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Complex Systems

Background:

• The driven lattice gas (DLG) model exhibits critical behavior relevant to systems with directed transport.
• Recent literature suggested the randomly driven lattice gas (RDLG) shares the same universality class as the DLG.
• Understanding universality classes is crucial for classifying phase transitions and predicting system behavior.

Purpose of the Study:

• To investigate the critical behavior of the two-dimensional randomly driven lattice gas (RDLG).
• To determine if the RDLG model belongs to the same universality class as the driven lattice gas with a constant drive (DLG).
• To provide novel evidence through finite-size scaling (FSS) analysis.

Main Methods:

• Finite-size scaling (FSS) analysis was employed to study the critical phenomena.
• Transverse observables, related to order-parameter fluctuations perpendicular to the drive direction, were analyzed.
• The study focused on specific lattice geometries, particularly rectangular lattices.

Main Results:

• The RDLG model does not belong to the same universality class as the DLG.
• Finite-size scaling functions for transverse observables in the RDLG differ from the mean-field behavior observed in the DLG.
• FSS is established only for specific rectangular lattices where one dimension scales quadratically with the other.
• The transverse Binder cumulant does not vanish at the critical point in the RDLG.

Conclusions:

• The RDLG model exhibits distinct critical behavior compared to the DLG.
• The findings challenge recent reports suggesting the models belong to the same universality class.
• The specific lattice geometry requirements for FSS highlight unique characteristics of the RDLG critical point.