  A random growth lattice filling model of percolation with touch and stop
growth rule is developed and studied numerically on a two dimensional square
lattice. Nucleation centers are continuously added one at a time to the empty
sites and the clusters are grown from these nucleation centers with a tunable
growth probability g. As the growth probability g is varied from 0 to 1 two
distinct regimes are found to occur. For g\le 0.5, the model exhibits
continuous percolation transitions as ordinary percolation whereas for g\ge 0.8
the model exhibits discontinuous percolation transitions. The discontinuous
transition is characterized by discontinuous jump in the order parameter,
compact spanning cluster and absence of power law scaling of cluster size
distribution. Instead of a sharp tricritical point, a tricritical region is
found to occur for 0.5 < g < 0.8 within which the values of the critical
exponents change continuously till the crossover from continuous to
discontinuous transition is completed.

Statistical Mechanics