Percolation RG

The key idea of a renormalization group (RG) transformation for percolation is to average over small parts of the lattice and then determine the effective value of $p$ for the new lattice. In this program we do the averaging by taking a $2 \times 2$ block of sites and replace it with a single occupied site if the occupied sites in the $2 \times 2$ block span vertically. Otherwise the blocked site is not occupied. Then the blocked spins are shown. This process is repeated using the blocked spins. The goal of the program is to allow the user to visualize the RG process.

Problem: Visual coarse-graining

Use Program PercolationRG to estimate the value of the percolation threshold. For example, confirm that for $p = 0.4$, the coarse-grained lattices almost always reduce to an unoccupied site. What happens for $p = 0.8$? How can you use the properties of the coarse-grained lattices to estimate $p_c$?


Problem 9.12 in Statistical and Thermal Physics: With Computer Applications, 2nd ed., Harvey Gould and Jan Tobochnik, Princeton University Press (2021).

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