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Phase transition of a two-dimensional binary spreading model
G Odor1, M C Marques, M A Santos
1Research Institute for Technical Physics and Materials Science, P. O. Box 49, H-1525 Budapest, Hungary.
Summary
This study reveals that higher-order approximations are crucial for understanding binary spreading processes. Numerical simulations support theoretical predictions about the upper critical dimension in this complex system.
Area of Science:
- Statistical Physics
- Complex Systems
Background:
- Binary spreading processes are fundamental models in statistical physics.
- Understanding phase transitions in these systems is key to predicting their collective behavior.
Purpose of the Study:
- To investigate the phase transition behavior of a 2D binary spreading process.
- To determine the necessity of higher-order mean-field approximations for accurate modeling.
- To explore the role of particle diffusion strength (D) on the transition.
Main Methods:
- Utilized N-body cluster mean-field approximations (N=3, 4).
- Conducted large-scale simulations of particle density.
- Analyzed scaling behavior of particle and pair densities.
Main Results:
- N>2 cluster mean-field approximations are required for consistent singular behavior.
- A continuous phase transition within a single universality class was observed for D in (0,1).
- Simulations confirmed mean-field scaling with logarithmic corrections, supporting d(c)=2.
- Directed percolation criticality was found at the D=0 endpoint.
Conclusions:
- The upper critical dimension for this binary spreading model is confirmed to be 2.
- Logarithmic corrections are essential for describing scaling behavior.
- The model exhibits different critical behaviors at different points along the transition line.