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Contact process in heterogeneous and weakly disordered systems.

C J Neugebauer¹, S V Fallert, S N Taraskin

¹Department of Chemistry, University of Cambridge, Cambridge, United Kingdom. cjn24@cam.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 13, 2006

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The contact process (CP) in disordered environments stays in the directed percolation universality class. However, quenched disorder may lead to continuously changing critical exponents, as shown by series expansion and Monte Carlo simulations.

Area of Science:

Statistical Physics
Complex Systems

Background:

The contact process (CP) is a fundamental model for epidemic spread and population dynamics.
Understanding CP behavior in complex environments is crucial for realistic modeling.

Purpose of the Study:

Investigate the critical behavior of the CP in heterogeneous, periodic, and weakly disordered environments.
Determine phase-separation lines and critical exponents.
Analyze the impact of quenched disorder on critical phenomena.

Main Methods:

Supercritical series expansion analysis.
Monte Carlo (MC) simulations.
Calculation of critical exponents beta and eta.

Main Results:

A general analytical expression for critical points in the weak-disorder limit was proposed and confirmed.

Related Experiment Videos

The CP in heterogeneous environments was found to belong to the directed percolation universality class.

Data for quenched disorder environments suggest a scenario of continuously changing critical exponents.

Conclusions:

The study clarifies the universality class of the contact process in various heterogeneous environments.
The findings highlight the distinct effects of weak versus quenched disorder on critical behavior.
Results provide insights into phase transitions in complex systems.