Editing Condensed matter physics (section)

===Phase transition===
{{Main|Phase transition}}

Phase transition refers to the change of phase of a system, which is brought about by change in an external parameter such as [[temperature]], [[pressure]], or [[molar composition]]. In a single-component system, a classical phase transition occurs at a temperature (at a specific pressure) where there is an abrupt change in the  order of the system. For example, when ice melts and becomes water, the ordered hexagonal crystal structure of ice is modified to a hydrogen bonded, mobile arrangement of water molecules.

In [[quantum phase transition]]s,  the temperature is set to [[absolute zero]], and the non-thermal control parameter, such as pressure or magnetic field,  causes the phase transitions when order is destroyed by [[quantum fluctuation]]s originating from the [[Heisenberg uncertainty principle]]. Here, the different quantum phases of the system refer to distinct [[ground state]]s of the [[Hamiltonian matrix]].  Understanding the behavior of quantum phase transition is important in the difficult tasks of explaining the properties of rare-earth magnetic insulators, high-temperature superconductors, and other substances.<ref name=Vojta2003/>

Two classes of phase transitions occur: ''first-order transitions'' and ''second-order'' or ''continuous transitions''. For the latter, the two phases involved do not co-exist at the transition temperature, also called the [[Critical point (thermodynamics)|critical point]].  Near the critical point, systems undergo critical behavior, wherein several of their properties such as [[correlation length]], [[specific heat]], and [[magnetic susceptibility]] diverge exponentially.<ref name=Vojta2003>{{cite journal |last=Vojta |first=Matthias |arxiv= cond-mat/0309604 |title=Quantum phase transitions |year=2003 |doi=10.1088/0034-4885/66/12/R01 |volume=66 |issue=12 |journal=Reports on Progress in Physics |pages=2069–2110|bibcode= 2003RPPh...66.2069V |citeseerx=10.1.1.305.3880 |s2cid=15806867 }}</ref>  These critical phenomena present serious challenges to physicists because normal [[Macroscopic scale|macroscopic]] laws are no longer valid in the region, and novel ideas and methods must be invented to find the new laws that can describe the system.<ref name=NRC1986>{{cite book |title = Condensed-Matter Physics, Physics Through the 1990s |publisher=National Research Council|year=1986 |url = http://www.nap.edu/catalog/626/an-overview-physics-through-the-1990s |isbn=978-0-309-03577-4 |doi=10.17226/626}}</ref>{{rp|75ff}}

The simplest theory that can describe continuous phase transitions is the [[Ginzburg–Landau theory]], which works in the so-called [[mean-field approximation]].  However, it can only roughly explain continuous phase transition for ferroelectrics and type I superconductors which involves long range microscopic interactions.  For other types of systems that involves short range interactions near the critical point, a better theory is needed.<ref name="University1989">{{cite book|author=Malcolm F. Collins Professor of Physics McMaster University|title=Magnetic Critical Scattering|publisher=Oxford University Press, USA|isbn=978-0-19-536440-8|date=1989-03-02}}</ref>{{rp|8–11}}

Near the critical point, the fluctuations happen over broad range of size scales while the feature of the whole system is scale invariant.  [[Renormalization group]] methods successively average out the shortest wavelength fluctuations in stages while retaining their effects into the next stage.  Thus, the changes of a physical system as viewed at different size scales can be investigated systematically.  The methods, together with powerful computer simulation, contribute greatly to the explanation of the critical phenomena associated with continuous phase transition.<ref name=NRC1986/>{{rp|11}}