Maze Proof and Statistical Mechanics

[jedishrfu]

https://www.quantamagazine.org/maze-proof-establishes-a-backbone-for-statistical-mechanics-20240207/

Imagine that a grid of hexagons, honeycomb-like, stretches before you. Some hexagons are empty; others are filled by a 6-foot tall column of solid concrete. The result is a maze of sorts. For over half a century, mathematicians have posed questions about such randomly generated mazes. How big is the largest web of cleared paths? What are the chances that there is a path from one edge to the center of the grid and back out again? How do those chances change as the grid swells in size, adding more and more hexagons to its edges?

 

[Hornbein]

https://www.quantamagazine.org/maze-proof-establishes-a-backbone-for-statistical-mechanics-20240207/

It's amazing that the critical value grows so slowly with the radius. The boundary between the two modes must be very sharp.