Editing Order and disorder (section)

==Quenched disorder==

In [[statistical physics]], a system is said to present '''quenched disorder''' when some parameters defining its behavior are [[random variable]]s which do not evolve with time. These parameters are said to be quenched or frozen. [[Spin glass]]es are a typical example. Quenched disorder is contrasted with [[annealed 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 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. Recently, rigorous methods have shown that in the [[Sherrington-Kirkpatrick model]], an archetypal spin glass model, the replica-based solution is exact. The [[Moment-generating function|generating functional formalism]], which relies on the computation of [[Functional integration|path integrals]], is a fully exact method but is more difficult to apply than the replica or cavity procedures in practice.

[[Image:Ordering.png|thumbnail|600px|center|Transition from disordered (left) to ordered (right) states]]