‘Stunning’ Percolation Proof Solves Decades-Old Puzzle About Phase Transitions

Percolation theory studies how fluids, gases, or other substances flow through networks, such as coffee grounds, filters, or city streets.

The concept originated in the 1940s when scientist Rosalind Franklin studied coal’s tiny holes to understand fluid flow through it.

In the 1950s, mathematicians Simon Broadbent and John Hammersley formalized the idea using a simple model: a grid of points connected by edges, where each edge is randomly opened or blocked.

If the probability of opening an edge is low, fluid remains in small, isolated pockets.

Once the probability crosses a critical threshold, fluid suddenly flows extensively, creating large connected areas—a phenomenon called a phase transition, similar to water turning to ice.

This critical threshold varies depending on the network’s structure, such as a square grid or a 3D lattice.