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The percolation phase transitions of two-dimensional lattice networks under ageneralized Achlioptas process (GAP) are investigated. During the GAP, twoedges are chosen randomly from the lattice and the edge with minimum product ofthe two connecting cluster sizes is taken as the next occupied bond with aprobability $p$. At $p=0.5$, the GAP becomes the random growth model and leadsto the minority product rule at $p=1$. Using the finite-size scaling analysis,we find that the percolation phase transitions of these systems with $0.5 \le p\le 1$ are always continuous and their critical exponents depend on $p$.Therefore, the universality class of the critical phenomena in two-dimensionallattice networks under the GAP is related to the probability parameter $p$ inaddition.

Continuous Percolation Phase Transitions of Two-dimensional Lattice Networks under a Generalized Achlioptas Process