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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 line s.
Condensed matter physics
Multivariate calculus
In mathematics, a critical point (or critical number) is a point on the domain of a function where the derivative is infinite, undefined, or equalSee also the disambiguation page title equality. In mathematics, two mathematical objects are considered equal if they are precisely the same in every way. This defines a binary predicate, equality denoted " "; x y iff x and y are equal. Equivalence in th to zero. The last kind is a stationary pointIn mathematics, particularly in calculus, a stationary point or inflection point is a point on the graph of a function where the tangent to the graph is parallel to the x axis or, equivalently, where the derivative of the function equals zero (known as a.
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 submersionIn mathematics, a differentiable map f from an m- manifold M to an n-manifold N is called a submersion if its differential df is an onto map at every point m of M :rk df(m dim N''. Examples include the projections in smooth vector bundles; and more genera).
