Percolia: Percolation Threshold
Thermodynamics & Statistical Physics arc, page 63 of 193. Back to The Pixelated Physics Universe
Who they are
Percolia has one line, and says it often: “At 59.27% the ideas finally connect.”
Percolia is a character of the Thermodynamics & Statistical Physics arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Site percolation on the square lattice has threshold pc ≈ 0.592746; below it no spanning cluster, above it one appears.
$$ \begin{gathered} p_c \approx 0.592746 \quad \text{(site percolation, square lattice)} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $p_c$ | percolation threshold (site occupation probability) | — |
Sources
Crossovers
Percolia meets Stilla (Anderson Localization). Percolia asks whether randomly placed sites form a connected path. Stilla adds a quantum twist: even when a path exists, interference between scattered waves can stop an electron from spreading along it.
Percolia meets Taulock (Critical Slowing Down). Percolia's threshold is a critical point too. Near p_c the cluster sizes diverge, just as correlation lengths do near Taulock's critical temperature.
Percolia meets Puckwarden (Darcy's Law Espresso). Puckwarden's espresso flows through a porous puck by Darcy's law. Percolia decides whether such a medium has connected pores at all: below the percolation threshold, no spanning path exists and the flow stops.
Wear the lore
Concept keywords: Percolation Threshold, Percolia, Thermodynamics & Statistical Physics, physics lore, Pixelated Physics