Fragmentation of percolation clusters in general dimensions

Area of Science:

• Statistical Physics
• Complex Systems
• Percolation Theory

Background:

• Percolation theory describes the formation of clusters in random networks.
• Binary fragmentation is a key process affecting the structure and dynamics of these clusters.
• Understanding scaling behavior is crucial for characterizing fragmentation phenomena.

Purpose of the Study:

• To investigate the scaling behavior of binary fragmentation for critical percolation clusters.
• To determine critical exponents governing fragmentation rate and cluster mass distribution.
• To validate theoretical scaling relations against simulation and expansion results.

Main Methods:

• Employed Monte Carlo simulations to model binary fragmentation.
• Utilized exact series expansions for analytical investigation.
• Calculated critical exponents lambda and phi.

Main Results:

• Obtained values for critical exponents lambda and phi in dimensions 2 through 9.
• Results demonstrate agreement with the conjectured scaling relation sigma=1+lambda-phi.
• The findings exclude alternative scaling relations proposed by other researchers.

Conclusions:

• The study confirms the validity of the Edwards et al. scaling relation for binary fragmentation.
• This provides strong evidence for the universality of scaling laws in percolation fragmentation.
• The findings contribute to a deeper understanding of critical phenomena in disordered systems.