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Inphysics, the termsorder anddisorder designate the presence or absence of somesymmetry orcorrelation in a many-particle system.^{[citation needed]}

Incondensed matter physics, systems typically are ordered at lowtemperatures; upon heating, they undergo one or severalphase transitions into less ordered states.Examples for such anorder-disorder transition are:

• themelting ofice: solid–liquid transition, loss ofcrystalline order;
• thedemagnetization ofiron by heating above theCurie temperature:ferromagnetic–paramagnetic transition, loss of magnetic order.

Thedegree of freedom that is ordered or disordered can be translational (crystalline ordering), rotational (ferroelectric ordering), or a spin state (magnetic ordering).

The order can consist either in a full crystallinespace group symmetry, or in a correlation. Depending on how the correlations decay with distance, one speaks oflong range order orshort range order.

If a disordered state is not inthermodynamic equilibrium, one speaks ofquenched disorder. For instance, aglass is obtained by quenching (supercooling) a liquid. By extension, other quenched states are calledspin glass,orientational glass. In some contexts, the opposite of quenched disorder isannealed disorder.

The strictest form of order in a solid islattice periodicity: a certain pattern (the arrangement of atoms in aunit cell) is repeated again and again to form a translationally invarianttiling of space. This is the defining property of acrystal. Possible symmetries have been classified in 14Bravais lattices and 230space groups.

Lattice periodicity implieslong-range order:^[1] if only one unit cell is known, then by virtue of the translational symmetry it is possible to accurately predict all atomic positions at arbitrary distances. During much of the 20th century, the converse was also taken for granted – until the discovery ofquasicrystals in 1982 showed that there are perfectly deterministic tilings that do not possess lattice periodicity.

Besides structural order, one may considercharge ordering,spin ordering,magnetic ordering, and compositional ordering. Magnetic ordering is observable inneutron diffraction.

It is athermodynamicentropy concept often displayed by a second-orderphase transition. Generally speaking, high thermal energy is associated with disorder and low thermal energy with ordering, although there have been violations of this. Ordering peaks become apparent in diffraction experiments at low energy.

Long-range order characterizes physicalsystems in which remote portions of the same sample exhibitcorrelated behavior.

This can be expressed as acorrelation function, namely thespin-spin correlation function:

${\displaystyle G(x,x^{\prime })=⟨s(x),s(x^{\prime })⟩.}$

wheres is the spin quantum number andx is the distance function within the particular system.

This function is equal to unity when${\displaystyle x=x^{\prime }}$ and decreases as the distance${\displaystyle |x-x^{\prime }|}$ increases. Typically, itdecays exponentially to zero at large distances, and the system is considered to be disordered. But if the correlation function decays to a constant value at large${\displaystyle |x-x^{\prime }|}$ then the system is said to possess long-range order. If it decays to zero as a power of the distance then it is called quasi-long-range order (for details see Chapter 11 in the textbook cited below. See alsoBerezinskii–Kosterlitz–Thouless transition). Note that what constitutes a large value of${\displaystyle |x-x^{\prime }|}$ is understood in the sense ofasymptotics.

Instatistical physics, a system is said to presentquenched disorder when some parameters defining its behavior arerandom variables which do not evolve with time. These parameters are said to be quenched or frozen.Spin glasses are a typical example. Quenched disorder is contrasted withannealed disorder in which the parameters are allowed to evolve themselves.

Mathematically, quenched disorder is more difficult to analyze than its annealed counterpart as averages over thermal noise and quenched disorder play distinct roles. Few techniques to approach each are known, most of which rely on approximations. Common techniques used to analyzed systems with quenched disorder include thereplica trick, based onanalytic continuation, and thecavity method, where a system's response to the perturbation due to an added constituent is analyzed. While these methods yield results agreeing with experiments in many systems, the procedures have not been formally mathematically justified. Recently, rigorous methods have shown that in theSherrington-Kirkpatrick model, an archetypal spin glass model, the replica-based solution is exact. Thegenerating functional formalism, which relies on the computation ofpath integrals, is a fully exact method but is more difficult to apply than the replica or cavity procedures in practice.

A system is said to presentannealed disorder when some parameters entering its definition arerandom variables, but whose evolution is related to that of thedegrees of freedom defining the system. It is defined in opposition to quenched disorder, where the random variables may not change their values.

Systems with annealed disorder are usually considered to be easier to deal with mathematically, since the average on the disorder and thethermal average may be treated on the same footing.

• Inhigh energy physics, the formation of thechiral condensate inquantum chromodynamics is an ordering transition; it is discussed in terms ofsuperselection.
• Entropy
• Topological order
• Impurity
• superstructure (physics)

• H Kleinert:Gauge Fields in Condensed Matter (ISBN 9971-5-0210-0, 2 volumes) Singapore: World Scientific (1989).
• Bürgi, H. B. (2000). "Motion and Disorder in Crystal Structure Analysis: Measuring and Distinguishing them".Annual Review of Physical Chemistry.51:275–296.Bibcode:2000ARPC...51..275B.doi:10.1146/annurev.physchem.51.1.275.PMID 11031283.
• Müller, Peter (2009)."5.067 Crystal Structure Refinement"(PDF). Cambridge: MIT OpenCourseWare. Retrieved13 October 2013.

• Statistical mechanics
• Crystallography

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