Order and disorder
In physics, the terms order and disorder designate the presence or absence of some symmetry or correlation in a many-particle system.Lattice periodicity implies long-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 of quasicrystals in 1982 showed that there are perfectly deterministic tilings that do not possess lattice periodicity.Long-range order characterizes physical systems in which remote portions of the same sample exhibit correlated behavior.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.In statistical physics, a system is said to present quenched disorder when some parameters defining its behavior are random variables which do not evolve with time.Common techniques used to analyzed systems with quenched disorder include the replica trick, based on analytic continuation, and the cavity 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.The generating functional formalism, which relies on the computation of path integrals, is a fully exact method but is more difficult to apply than the replica or cavity procedures in practice.
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