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In [[thermodynamics]], a '''phase transition''' is the transformation of a thermodynamic system from one [[phase]] to another.  At phase-transition point, physical properties may undergo abrupt change- for instance, volume of the two phases may be vastly different.  As an example imagine transition of liquid water into vapour at boiling point.   

In [[thermodynamics]], a '''phase transition''' is the transformation of a thermodynamic system from one [[phase]] to another.  At phase-transition point, physical properties may undergo abrupt change- for instance, volume of the two phases may be vastly different.  As an example imagine transition of liquid water into vapour at boiling point.   

   

   

In the English vernacular, the term is most commonly used to describe transitions between [[solid]], [[liquid]] and [[gas]]eous [[states of matter]], in rare cases including [[Plasma (physics)|plasma]]. Phase transitions happen when the [[Thermodynamic free energy|free energy]] of a system is [[analytic function|non-analytic]] for some choice of thermodynamic variables - see [[phases]]. This non-analyticity generally stems from the interactions of an extremely large number of particles in a system, and does not appear in systems that are too small.

In the [[English]] vernacular, the term is most commonly used to describe transitions between [[solid]], [[liquid]] and [[gas]]eous [[states of matter]], in rare cases including [[Plasma (physics)|plasma]]. Phase transitions happen when the [[Thermodynamic free energy|free energy]] of a system is [[analytic function|non-analytic]] for some choice of thermodynamic variables - see [[phases]]. This non-analyticity generally stems from the interactions of an extremely large number of particles in a system, and does not appear in systems that are too small.

To put it simply, at phase-transition point (for instance, [[boiling point]] for water) the two phases of water - [[liquid]] and [[vapour]] have identical free energies and therefore are equally likely to exist. Below the boiling point, liquid-water is more stable state of the two. At [[boiling point]] [[liquid]] and [[vapour]] are equally stable and above boiling point [[vapour]] is more stable than liquid state of [[water]].

At phase-transition point (for instance, [[boiling point]] for water) the two phases of water - [[liquid]] and [[vapour]] have identical free energies and therefore are equally likely to exist. Below the boiling point, liquid-water is more stable state of the two. At [[boiling point]] [[liquid]] and [[vapour]] are equally stable and above boiling point [[vapour]] is more stable than liquid state of [[water]].

== Magnetic phases ==

== Magnetic phases ==

Often also ''magnetic'' phases are used as the basis of a theory, and for introductory motivation. However, usually these are similar to the  well-known liquid (ferromagnetic) or gaseous  paramagnetic) phases, as can be seen by the two equivalent interpretations, the ''magnetic'' one ("up" or "down" spins) or the ''lattice-gas'' interpretation ("occupied" or "unoccupied" sites) of a prominent binary model, the [[Ising model]].  

Often also ''magnetic'' phases are used as the basis of a theory, and for introductory motivation. However, usually these are similar to the  well-known liquid (ferromagnetic) or gaseous  paramagnetic) phases, as can be seen by the two equivalent interpretations, the ''magnetic'' one ("up" or "down" spins) or the ''lattice-gas'' interpretation ("occupied" or "unoccupied" sites) of a prominent binary model, the [[Ising model]].  

== Properties of phase transitions ==

== Properties of phase transitions ==

=== Critical points ===

=== Critical points ===

In any system containing liquid and gaseous phases, there exists a special combination of pressure and temperature, known as the [[critical point]],  at which the transition between liquid and gas becomes a second-order transition. Near the critical point, the fluid is sufficiently hot and compressed that the distinction between the liquid and gaseous phases is almost non-existent.

In any system containing liquid and gaseous phases, there exists a special combination of pressure and temperature, known as the [[critical point]],  at which the transition between liquid and gas becomes a second-order transition. Near the critical point, the fluid is sufficiently hot and compressed that the distinction between the liquid and gaseous phases is almost non-existent.

This is associated with the phenomenon of [[critical opalescence]], a milky appearance of the liquid, due to density fluctuations at all possible wavelengths (including those of visible light).

This is associated with the phenomenon of [[critical opalescence]], a milky appearance of the liquid, due to density fluctuations at all possible wavelengths (including those of visible light).

=== Symmetry ===

=== Symmetry ===

Phase transitions often (but not always) take place between phases with different [[symmetry]]. Consider, for example, the transition between a fluid (i.e. liquid or gas) and a [[crystal|crystalline solid]]. A fluid, which is composed of atoms arranged in a disordered but homogeneous manner, possesses continuous translational symmetry: each point inside the fluid has the same properties as any other point. A crystalline solid, on the other hand, is made up of atoms arranged in a regular [[crystal structure|lattice]]. Each point in the solid is ''not'' similar to other points, unless those points are displaced by an amount equal to some lattice spacing.

Phase transitions often (but not always) take place between phases with different [[symmetry]]. Consider, for example, the transition between a fluid (i.e. liquid or gas) and a [[crystal|crystalline solid]]. A fluid, which is composed of atoms arranged in a disordered but homogeneous manner, possesses continuous translational symmetry: each point inside the fluid has the same properties as any other point. A crystalline solid, on the other hand, is made up of atoms arranged in a regular [[crystal structure|lattice]]. Each point in the solid is ''not'' similar to other points, unless those points are displaced by an amount equal to some lattice spacing.

Symmetries which are only present at low temperatures are called [[accidental symmetry|accidental symmetries]].  For example, a symmetry which is broken by a process which requires a lot of energy, such as the creation of heavy [[virtual particles]], is an accidental symmetry at temperatures sufficiently low that this process is suppressed.

Symmetries which are only present at low temperatures are called [[accidental symmetry|accidental symmetries]].  For example, a symmetry which is broken by a process which requires a lot of energy, such as the creation of heavy [[virtual particles]], is an accidental symmetry at temperatures sufficiently low that this process is suppressed.

==References==

==References==

#Chang, R., Chemistry, 7th Ed, McGraw-Hill (2002)

#Chang, R., Chemistry, 7th Ed, McGraw-Hill (2002)

#McNaught and A. Wilkinson, ed. Compendium of Chemical Terminology (commonly called The Gold Book). IUPAC. ISBN 0-86542-684-8. http://www.iupac.org/goldbook/O04323.pdf. Retrieved on 2007-10-23.  

#McNaught and A. Wilkinson, ed. Compendium of Chemical Terminology (commonly called The Gold Book). IUPAC. ISBN 0-86542-684-8. https://www.iupac.org/goldbook/O04323.pdf. Retrieved on 2007-10-23.  

#Chaisson, “Cosmic Evolution”, Harvard, 2001

#Chaisson, “Cosmic Evolution”, Harvard, 2001

#David Layzer, Cosmogenesis, The Development of Order in the Universe", Oxford Univ. Press, 1991

#David Layzer, Cosmogenesis, The Development of Order in the Universe", Oxford Univ. Press, 1991

===General references===

===General references===

*Philip Warren Anderson, ''Basic Notions of Condensed Matter Physics'', Perseus Publishing (1997).

*Philip Warren Anderson, ''Basic Notions of Condensed Matter Physics'', Perseus Publishing (1997).

*Krieger, Martin H., ''Constitutions of matter : mathematically modelling the most everyday of physical phenomena'', University of Chicago Press, 1996.  Contains a detailed pedagogical discussion of Onsager's solution of the 2-D Ising Model.

*Krieger, Martin H., ''Constitutions of matter : mathematically modelling the most everyday of physical phenomena'', University of Chicago Press, 1996.  Contains a detailed pedagogical discussion of Onsager's solution of the 2-D Ising Model.

*Lev Davidovich Landau and Evgeny Mikhailovich Lifshitz, ''Statistical Physics Part 1'', vol. 5 of ''Course of Theoretical Physics'', Pergamon, 3rd Ed. (1994).

*Lev Davidovich Landau and Evgeny Mikhailovich Lifshitz, ''Statistical Physics Part 1'', vol. 5 of ''Course of Theoretical Physics'', Pergamon, 3rd Ed. (1994).

*Hagen Kleinert, ''Critical Properties of φ⁴-Theories'', [http://www.worldscibooks.com/physics/4733.html World Scientific (Singapore, 2001)];  Paperback ISBN 9810246595'' (readable online [http://www.physik.fu-berlin.de/~kleinert/b8 here]).''

*Hagen Kleinert, ''Critical Properties of φ⁴-Theories'', [https://www.worldscibooks.com/physics/4733.html World Scientific (Singapore, 2001)];  Paperback ISBN 9810246595'' (readable online [https://www.physik.fu-berlin.de/~kleinert/b8 here]).''

*[[Hagen Kleinert and Verena Schulte-Frohlinde, ''Gauge Fields in Condensed Matter'', Vol. I,  "[[SUPERFLOW]] AND [[VORTEX LINES]]; Disorder Fields, Phase Transitions,", pp. 1--742, [http://www.worldscibooks.com/physics/0356.htm World Scientific (Singapore, 1989)];  Paperback ISBN 9971-5-0210-0 '' (readable online  [http://www.physik.fu-berlin.de/~kleinert/kleiner_reb1/contents1.html here])

*[[Hagen Kleinert and Verena Schulte-Frohlinde, ''Gauge Fields in Condensed Matter'', Vol. I,  "[[SUPERFLOW]] AND [[VORTEX LINES]]; Disorder Fields, Phase Transitions,", pp. 1--742, [https://www.worldscibooks.com/physics/0356.htm World Scientific (Singapore, 1989)];  Paperback ISBN 9971-5-0210-0 '' (readable online  [https://www.physik.fu-berlin.de/~kleinert/kleiner_reb1/contents1.html here])

*Schroeder, Manfred R., ''Fractals, chaos, power laws : minutes from an infinite paradise'', New York: W.H. Freeman, 1991.  Very well-written book in "semi-popular" style -- not a textbook -- aimed at an audience with some training in mathematics and the physical sciences.  Explains what scaling in phase transitions is all about, among other things.

*Schroeder, Manfred R., ''Fractals, chaos, power laws : minutes from an infinite paradise'', New York: W.H. Freeman, 1991.  Very well-written book in "semi-popular" style -- not a textbook -- aimed at an audience with some training in mathematics and the physical sciences.  Explains what scaling in phase transitions is all about, among other things.

== External links ==

== External links ==

* [http://www.ibiblio.org/e-notes/Perc/contents.htm Interactive Phase Transitions on lattices] with Java applets

* [https://www.ibiblio.org/e-notes/Perc/contents.htm Interactive Phase Transitions on lattices] with Java applets

[[Category: Physics]]

[[Category: Physics]]

[[Category: Chemistry]]

[[Category: Chemistry]]