Probability of Incipient Spanning Clusters in Critical Two-Dimensional Percolation
L.N. Shchur, S.S. Kosyakov (Landau Institute for Theoretical, Physics, Chernogolovka, Russia)
TL;DR
This paper investigates the probability of multiple spanning clusters in 2D percolation at criticality using Monte Carlo simulations, confirming recent exact formulas for different boundary conditions.
Contribution
It provides numerical validation of exact theoretical formulas for spanning cluster probabilities in 2D percolation.
Findings
Monte Carlo probabilities match Cardy's exact formulas
Results are consistent for free and periodic boundary conditions
Supports the validity of recent theoretical developments in 2D percolation
Abstract
The probability of simultaneous occurence of at least k spanning clusters has been studied by Monte Carlo simulations on the 2D square lattice at the bond percolation threshold Pc=1/2. The calculated probabilities for free boundary conditions and periodic boundary conditions are in a very good coincidence with the exact formulae developed recently by Cardy.
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