Crossover behavior of conductivity in a discontinuous percolation model

Area of Science:

• Physics
• Materials Science
• Statistical Mechanics

Background:

• Percolation theory describes conductivity changes with bond density.
• Continuous percolation transitions are well-understood.
• Discontinuous percolation transitions and their conductivity behavior remain less explored.

Purpose of the Study:

• Investigate conductivity in discontinuous percolation models.
• Analyze conductivity behavior under a suppressive external bias.
• Develop an analytical model for conductivity in such systems.

Main Methods:

• Utilized a discontinuous percolation model.
• Applied a suppressive external bias.
• Employed effective medium theory for analytical calculations.
• Validated results with simulation data.

Main Results:

• Derived an analytical expression for conductivity.
• Observed a crossover in conductivity behavior beyond the percolation threshold.
• The transition shifted from drastic to smooth increase.
• Analytic expression accurately matched simulation data.

Conclusions:

• Effective medium theory successfully models conductivity in discontinuous percolation.
• External bias induces a crossover in conductivity behavior.
• The findings provide insights into complex system conductivity.