First-order transition in a percolation model with nucleation and preferential growth.

Area of Science:

• Complex systems
• Statistical physics
• Network science

Background:

• Percolation theory models random networks and phase transitions.
• Nucleation and preferential growth introduce new dynamics to standard percolation models.
• Understanding cluster formation is crucial in fields like materials science and epidemiology.

Purpose of the Study:

• To investigate the phase transitions in a modified percolation model incorporating nucleation and preferential growth.
• To analyze the impact of the growth parameter (g0) and initial seed concentration (ρ) on spanning cluster properties.
• To characterize the transition from continuous to discontinuous phase transitions.

Main Methods:

• Modification of the standard percolation model to include nucleation and size-dependent preferential growth.
• Systematic variation of the growth parameter (g0) and initial seed concentration (ρ).
• Analysis of spanning cluster formation and transition types (continuous vs. first-order).

Main Results:

• The model exhibits first-order transitions dependent on g0 and ρ.
• A coexistence region of percolative and nonpercolative clusters appears as ρ decreases from the percolation threshold (pc).
• At low ρ (≤0.05) and g0 > pc, compact spanning clusters form, leading to discontinuous, first-order transitions.

Conclusions:

• The modified percolation model demonstrates a rich phase diagram with tunable transition types.
• Preferential growth and nucleation significantly alter cluster formation compared to standard percolation.
• The findings provide insights into the emergence of compact structures and abrupt transitions in complex systems.