concept

Phase transition

A sudden, qualitative change in the state of a system when a control parameter crosses a critical value — like water freezing into ice at exactly 0°C. Unlike a gradual change, a phase transition has a sharp break: just below the point the system is one kind of thing, just above it a qualitatively different kind, with no gentle middle. The idea reaches far beyond thermal physics: the shattering of a network at its percolation threshold is a genuine phase transition in the deepest mathematical sense — which is why a network does not "weaken gradually" but survives almost intact and then collapses entirely in a single instant.