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In [[condensed matter physics]], dealing with the macroscopic physical properties of matter, a '''tricritical point''' is a point in the [[phase diagram]] of a system at which
[[Phase equilibrium|three-phase coexistence]] terminates.<ref>B. Widom, ''Theory of Phase Equilibrium'', J. Phys. Chem '''1996''', 100, 13190-13199</ref> This definition is clearly
parallel to the definition of an ordinary [[critical point (thermodynamics)|critical point]] as the point at which two-phase coexistence terminates.

A point of three-phase coexistence is termed a [[triple point]] for a one-component system, since, from [[Gibbs' phase rule]], this condition is only achieved for a single point in the phase diagram
(''F''=2-3+1=0). For tricritical points to be observed, one needs a mixture with more components. It can be shown<ref>''ibid''.</ref> that '''three''' is the minimum number of components for which these points can appear. In this case, one may have a two-dimensional region of three-phase coexistence
(''F''=2-3+3=2) (thus, each point in this region corresponds to a [[triple point]]). This region will terminate in two critical lines of phase coexistence; these two critical lines may then terminate at a single tricritical point. This point is therefore "twice critical", since it belong to two critical branches. Indeed, its [[critical behavior]] is different from that of a conventional critical point: the [[upper critical dimension]] is lowered from d=4 to d=3 so the [[landau theory|classical exponents]] turn out to apply for real systems in three dimensions (but not for systems whose spatial dimension is 2 or lower).

It seems more convenient {{Citation needed|date=April 2009}} experimentally to consider mixtures with four components for which one thermodynamic variable (usually the pressure or the volume) is kept fixed. The situation then reduces to the one described for mixtures of three components.

Historically, it was for a long time unclear whether a superconductor
undergoes a first- or a second-order phase transition.
The question was finally settled
in 1982.<ref>
{{cite journal
| title = Disorder Version of the Abelian Higgs Model and the Order of the Superconductive Phase Transition
| author = [[Hagen Kleinert|H. Kleinert]]
| journal = Lett. Nuovo Cimento
| volume = 35
| pages = 405–412
| year = 1982
| doi = 10.1007/BF02754760
| url = http://www.physik.fu-berlin.de/~kleinert/97/97.pdf}}
</ref> If the Ginzburg-Landau parameter <math>\kappa</math> that distinguishes [[Type I superconductor|type-I]] and
[[Type II superconductor|type-II]] superconductors (see also [[Ginzburg–Landau theory|here]])
is large enough, vortex fluctuations
becomes important
which drive the transition to second order
.<ref>
{{cite journal
| title = Vortex Origin of Tricritical Point in Ginzburg-Landau Theory
| author = [[Hagen Kleinert|H. Kleinert]]
| journal = Europh. Letters
| volume = 74
| pages = 889
| year = 2006
| doi = 10.1209/epl/i2006-10029-5
| url = http://www.physik.fu-berlin.de/~kleinert/360/360.pdf|arxiv = cond-mat/0509430 |bibcode = 2006EL.....74..889K }}
</ref>
The tricitical point lies at
roughly
<math>\kappa=0.76/\sqrt{2}</math>, i.e., slightly below the value <math>\kappa=1/\sqrt{2}</math>
where [[Type II superconductor|type-I]] goes over into [[Type II superconductor|type-II]] superconductor.
The prediction was confirmed in 2002 by [[Computer simulation|Monte Carlo computer simulations]].<ref>
{{cite journal
| title = Vortex interactions and thermally induced crossover from type-I to type-II superconductivity
| author = J. Hove, S. Mo, A. Sudbo
| journal = Phys. Rev.
| volume = B 66
| pages = 064524
| year = 2002
| doi = 10.1103/PhysRevB.66.064524
| url = http://www.physik.fu-berlin.de/~kleinert/papers/sudbotre064524.pdf
| bibcode=2002PhRvB..66f4524H|arxiv = cond-mat/0202215 }}
</ref>

==References==
<references/>

[[Category:Phase transitions]]
[[Category:Critical phenomena]]
[[Category:Condensed matter physics]]

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en>BattyBot: removed Template:Multiple issues & general fixes using AWB (9866)