## SCL seminar by Danica Stojiljkovic

On 11 June 2010, SCL's Danica Stojiljkovic held the first of two seminar talks entitled "Introduction to Percolation Theory". The focus of the talk was the main concepts of the percolation theory which represents one of the simplest models of a disordered system. The systems concidered are different kinds of n Dim lattices where each site can either be occupied with probability p, or empty with probability 1-p. Two sites belong to the same cluster if they are connected by a path of nearest neighbor sites. Occupied and empty sites may stand for very different physical properties. For example sites can represent electrical conductors and insulators, and that electrical current can flow between nearest neighbor conductor sites. At low concentration p, the conductor sites are either isolated or form small clusters of nearest neighbor sites. Two conductor sites belong to the same cluster if they are connected by a path of nearest neighbor conductor sites, and a current can flow between them. At low p values, the mixture is an insulator, since a conducting path connecting opposite edges of the lattice does not exist. At large p values, on the other hand, many conduction paths between opposite edges exist, where electrical current can flow, and the mixture is a conductor. At some concentration in between, therefore, a threshold concentration pc must exist where for the first time electrical current can percolate from one edge to the other. Below pc, we have an insulator, above pc we have a conductor. The threshold concentration is called the percolation threshold, or, since it separates two different phases, the critical concentration.

Danica presented different kind of Percolation, and various parameters that quantify these processes.