ICTS

The percolation transition (PT), that is, the formation of a giant cluster on a macroscopic scale, is known as one of the most robust continuous geometrical phase transitions. However, a variety of new percolation models has been introduced at the beginning of this century and also a variety of new features are reported. Whereas, the nature of explosive percolation has been the topic of intense debate for the past few years. Therefore, we develope a number of lattice models incorporating the essential ingredients and associating more than one parameter in order to realize percolation as a first-order transition. The models developed represent both equilibrium behavior as well as non-equilibrium growth processes. Staring with a simple two parameter model with random processes and incorporating nucleation and coagulation it was possible to exhibit a crossover from continuous to discontinuous transition with a tricritical region in most of the models.