Scaling Properties, Fractals, and the Renormalization Group Approach to Percolation

Glossary Cluster Clusters are sets of occupied neighbouring sites. Critical exponents At a critical point or second-order phase transition, many quantities diverge or vanish with a power law of the distance from this critical point; the critical exponent is the exponent for this power law. Fractals Fractals have a mass varying with some power of their linear dimension. The exponent of this power law is called the fractal dimension and is smaller than the dimension of the space. Percolation Each site of a large lattice is randomly occupied or empty. Renormalization A cell of several sites, atoms, or spins is approximated by one single site etc. At the critical point, these supersites behave like the original sites, and the critical point thus is a fixed point of the renormalisation.