# Phase transition

From Encyclopedia of Mathematics

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).

#### References

[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) |

#### Comments

#### References

[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: http://encyclopediaofmath.org/index.php?title=Phase_transition&oldid=19100

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098