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
three-phase coexistence terminates. This definition is clearly parallel to the definition of an ordinary
critical point as the point at which two-phase coexistence terminates.
A point of three-phase coexistence is termed a
triple point
In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium.. It is that temperature and pressure at which the sub ...
for a one-component system, since, from
Gibbs' phase rule
In thermodynamics, the phase rule is a general principle governing "pVT" systems, whose thermodynamic states are completely described by the variables pressure (), volume () and temperature (), in thermodynamic equilibrium. If is the number of d ...
, 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 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 two-phase coexistence; these two critical lines may then terminate at a single tricritical point. This point is therefore "twice critical", since it belongs to two critical branches.
Indeed, its
critical behavior
In physics, critical phenomena is the collective name associated with the
physics of critical points. Most of them stem from the divergence of the
correlation length, but also the dynamics slows down. Critical phenomena include scaling relation ...
is different from that of a conventional critical point: the upper
critical dimension
In the renormalization group analysis of phase transitions in physics, a critical dimension is the dimensionality of space at which the character of the phase transition changes. Below the lower critical dimension there is no phase transition. ...
is lowered from d=4 to d=3 so the
classical exponents turn out to apply for real systems in three dimensions (but not for systems whose spatial dimension is 2 or lower).
Solid state
It seems more convenient 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. If the Ginzburg–Landau parameter
that distinguishes
type-I and
type-II superconductors (see also
here
Here is an adverb that means "in, on, or at this place". It may also refer to:
Software
* Here Technologies, a mapping company
* Here WeGo (formerly Here Maps), a mobile app and map website by Here Technologies, Here
Television
* Here TV (form ...
) is large enough, vortex fluctuations become important which drive the transition to ''second'' order.
The tricritical point lies at roughly
, i.e., slightly below the value
where type-I goes over into type-II superconductor. The prediction was confirmed in 2002 by Monte Carlo
computer simulations
Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be dete ...
.
[
]
References
Phase transitions
Critical phenomena
{{CMP-stub