Percolation and universality
Percolation and universality
Percolation deals with global properties of random configurations of local objects. While simple to implement in models, understanding percolation requires skill in pattern recognition and analysis. A cluster recognition algorithm is developed to obtain properties of percolation models. The fractal nature of a percolating system is discussed, along with general features of fractals. Scaling laws and critical exponents, which are central features of modern approaches to complex systems, are also introduced and illustrated with percolating systems. The important concept of a correlation function is also used to characterize these systems. Finally, the insensitivity of large classes of model systems with respect to short range dynamics, known as universality, is discussed in the context of percolation. This is illustrated with the modern concepts of coarse graining and the renormalization group.
Keywords: percolation theory, fractals, scaling laws, renormalization, coarse graining, universality, cluster algorithms
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