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 gaseous states of matter, in rare cases including plasma. Phase transitions happen when the free energy of a system is 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.
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.
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
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).
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 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 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.
Generally, we may speak of one phase in a phase transition as being more symmetrical than the other. The transition from the more symmetrical phase to the less symmetrical one is a symmetry-breaking process. In the fluid-solid transition, for example, we say that continuous translation symmetry is broken.
The ferromagnetic transition is another example of a symmetry-breaking transition, in this case the symmetry under reversal of the direction of electric currents and magnetic field lines. This symmetry is referred to as "up-down symmetry" or "time-reversal symmetry". It is broken in the ferromagnetic phase due to the formation of magnetic domains containing aligned magnetic moments. Inside each domain, there is a magnetic field pointing in a fixed direction chosen spontaneously during the phase transition. The name "time-reversal symmetry" comes from the fact that electric currents reverse direction when the time coordinate is reversed.
The presence of symmetry-breaking (or nonbreaking) is important to the behavior of phase transitions. It was pointed out by Landau that, given any state of a system, one may unequivocally say whether or not it possesses a given symmetry. Therefore, it cannot be possible to analytically deform a state in one phase into a phase possessing a different symmetry. This means, for example, that it is impossible for the solid-liquid phase boundary to end in a critical point like the liquid-gas boundary. However, symmetry-breaking transitions can still be either first- or second-order.
Typically, the more symmetrical phase is on the high-temperature side of a phase transition, and the less symmetrical phase on the low-temperature side. This is certainly the case for the solid-fluid and ferromagnetic transitions. This happens because the Hamiltonian of a system usually exhibits all the possible symmetries of the system, whereas the low-energy states lack some of these symmetries (this phenomenon is known as spontaneous symmetry breaking). At low temperatures, the system tends to be confined to the low-energy states. At higher temperatures, thermal fluctuations allow the system to access states in a broader range of energy, and thus more of the symmetries of the Hamiltonian.
Symmetries which are only present at low temperatures are called 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.
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- Chaisson, “Cosmic Evolution”, Harvard, 2001
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- 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.
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- Hagen Kleinert, Critical Properties of φ4-Theories, World Scientific (Singapore, 2001); Paperback ISBN 9810246595 (readable online here).
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- 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.
- Interactive Phase Transitions on lattices with Java applets