Phase transition

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A physical phenomenon that occurs in macroscopic systems and consists in the following. In certain equilibrium states of the system an arbitrary small influence leads to a sudden change of its properties: the system passes from one homogeneous phase to another. Mathematically, a phase transition is treated as a sudden change of the structure and properties of the so-called Gibbs distributions describing the equilibrium states of the system, for arbitrary small changes of the parameters determining the equilibrium (cf. Gibbs distribution; Gibbs statistical aggregate).


[1] L.D. Landau, E.M. Lifshitz, "Statistical physics" , Pergamon (1980) (Translated from Russian)
[2] Ya.G. Sinai, "Theory of phase transitions" , Pergamon (1982) (Translated from Russian)



[a1] H.L. Frisch (ed.) J.L. Lebowitz (ed.) , The equilibrium theory of classical fluids , Benjamin (1964)
[a2] H.E. Stanley, "Introduction to phase transitions and critical phenomena" , Pergamon (1971)
How to Cite This Entry:
Phase transition. R.A. Minlos (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098