Rounding Effects in Systems with Static Disorder

Condensed matter physics often has to consider systems with static disorder [6], [7], i.e. with impurities, dislocations, substitutions etc. which vary from sample to sample (thus introducing disorder) but which do not exhibit thermal fluctuations on relevant time scales (hence the word static). To account for such disorder mathematically one often uses lattice spin systems with random parameters in the interaction (e.g. random magnetic fields or random coupling constants). For each fixed realization of these parameters one then obtains a spin system in which the usual quantities of physical interest — magnetization, free energy etc. — can be calculated. Random parameters of this type are often called quenched, to stress the fact that they remain constant during the calculation of spin averages — corresponding to the static nature of the disorder in the modelled physical system.