Quenched disorder

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In statistical physics, a system is said to present quenched disorder when some parameters defining its behaviour are random variables which do not evolve with time, i.e.: they are quenched or frozen. As a typical example, we may cite spin glasses. It is opposite to annealed disorder, where the random variables are allowed to evolve themselves.

In mathematical terms, the quenched disorder is harder to analyze than its annealed counterpart, since the thermal and the noise averaging play very different roles. In fact, the problem is so hard that few techniques to approach each are known, most of them relying on approximations. The most used is Replica Theory, a technique based on a mathematical analytical continuation known as the replica trick which, although giving results in accord with experimentations in a large range of problems, is not generally proven to be a rigorous mathematical procedure. More recently it has been shown by rigorous methods, however, that at least in the archetypical spin-glass model (the so-called Sherrington-Kirkpatrick model) the replica based solution is indeed exact; this area is still subject of research. The second most used technique in this field is generating functional analysis. This method is based on path integrals, and is in principle fully exact, although generally more difficult to apply than the replica procedure.