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Critical behavior of the two- and three-dimensional contact replication processes
1Departamento de Física, Universidade Federal de Viçosa, 36571-000, Viçosa, Minas Gerais, Brazil. silviojr@ufv.br
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
Summary
Contact replication processes (CRP) in two and three dimensions were simulated. The 2D CRP belongs to the directed percolation universality class, while the 3D CRP suggests an upper critical dimension of 3.
Area of Science:
- Statistical Physics
- Complex Systems Modeling
Background:
- The contact replication process (CRP) is a fundamental model for monoclonal reproduction.
- Understanding the dimensional dependence of CRP critical behavior is crucial for theoretical models.
Purpose of the Study:
- To analyze the two- and three-dimensional contact replication processes (CRP) using Monte Carlo simulations.
- To determine the universality class and critical exponents for different dimensions.
Main Methods:
- Intensive Monte Carlo simulations were employed to model the CRP.
- Occupation rates were equally distributed among empty nearest neighbor sites.
Main Results:
- The two-dimensional CRP falls within the directed percolation universality class.
- The critical rate for the 2D absorbing state transition was found to be lambda_c = 1.08320(7).
- The three-dimensional CRP exhibits critical exponents matching the four-dimensional original contact process.
Conclusions:
- The CRP model demonstrates a distinct upper critical dimension (d_c) of 3.
- This finding has significant implications for understanding phase transitions in spatially extended systems.