Critical point - Definition and Overview

In chemistry, a critical point is the conditions (temperature, pressure) at which the liquid state of the matter ceases to exist. As a liquid is heated, its density decreases while the density of the vapor being formed increases. The liquid and vapor densities become closer and closer to each other until the critical temperature is reached where the two densities are equal and the liquid-gas line or phase boundary disappears.

In physics, it is sometimes taken to mean the point of a second order phase transition.

According to Renormalization Group Theory, the defining property of criticality is that the natural lengthscale characteristic of the structure of the physical system, the so-called correlation length ξ, becomes infinite. There are also lines in phase space along which this happens: these are Critical lines.

In mathematics, a critical point (or critical number) is a point on the domain of a function where the derivative is infinite, undefined, or equal to zero. The last kind is a stationary point.

In higher dimensions, and for functions of several variables, this concept becomes a point where the rank of the derivative (Jacobian matrix) is not maximal (see submersion).