On: Going Critical

[perlgeek]

Very cool!

As a small translation aid, when physicists talk about criticality, they tend to talk about "dimensions" instead of "degree".

In a one-dimensional system, a line, you can have at most two nearest neighbors, in a two-dimensional system 4, 3D has 6 neighbors, and so on.

Physicists have no trouble talking about fractional dimensions either, which can be realized in surfaces, fractal-like substances and so on.

Dimensions higher than 3 are achieved when interactions between non-nearest neighbors are relevant.

[atemerev → perlgeek]

While these examples use lattices for simplicity, the terminology comes from network science and graph theory, where there are degrees and connections, and "dimensions" mean something else (multi-dimensional networks is a rich theory on its own).