Discontinuous percolation transition search for new models and scaling theory

Abstract

Percolation has long served as a model for diverse phenomena The percolation transition is known as one of the most robust continuous geometrical phase transitions However in the recent past a series of new models with abrupt percolation transitions have been observed in complex systems Whereas the nature of explosive percolation transitions has been the topic of intense debate for the past few years In this thesis a number of lattice models are developed incorporating the essential ingr