Discontinuous percolation transition: Search for new models and scaling theory

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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 ingredients like nucleation and growth in order to realize percolation as a first-order transition in static equilibrium properties of clusters as well as in a non-equilibrium growth process. First, a new two-parameter percolation model (TPPM) with simultaneous growth of multiple clusters is developed. The model has an expand parameter space than that of original percolation model. Percolation transition is determined by the final static configurations of spanning clusters. It is found that the values of the critical exponents describing the scaling functions at the criticality in this model are that of original percolation for all values of ρ and the transitions belong to the same universality class of percolation. Secondly, the model is improved by introducing suppressed cluster growth incorporating a cluster size dependent dynamic growth probability.
Supervisor: Sitangshu Bikas Santra