_{Sometimes disorder is used as a synonym of randomness, in which case, what I describe here is called quenched disorder.}

Disorder, I think, refers to a particular kind of randomness in a system, in which there may be spatial randomness, but the random variables are fixed, for each instance of the system. This is in contrast to spatio-temporal disorder due to Temperature, as described by Statistical physics.

As means of illustration, if the disorder is in a parameter in the Hamiltonian, for instance in some couplings (as in Spin glasses), it means that, before analyzing the Hamiltonian, we first determine all the couplings by coin tossing, or what-ever other method we choose; after that, they remain fixed for all time. This process leads to a particular choice, or realization, of the couplings, and thus a particular realization of the Hamiltonian, or the system.

Disorder affects the behaviour if the system is finite, or if the disorder is non-Self-averaging. A system that has disorder, specially if the disorder affects its behaviour, is referred to as a Disordered system.

Types of disorder

There are two types of disorder:

• Annealed disorder: disorder of a system at thermal equilibrium. This can be physically achieved by cooling the system down sufficiently slowly so that the system is in quasi-equilibrium at all times.
• Quenched disorder: disorder of a system in which the disordered variable is out of equilibrium. For instance in Glasses. This can be achieved by cooling sufficiently rapidly, so that a random configuration is quenched, and stays so, due to extremely large relaxation times.
• One could also have a combination of the two.