Random field systems

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Abstract
Spin models in weak random fields are good representations of a large number of impure compounds which undergo magnetic or structural transitions. From a theoretical point of view these systems exhibit frustration on a mesoscopic scale and take therefore an indermediate position between (spin) glasses and unfrustrated (diluted) disordered systems. A simple but rigorously proven domain argument shows that long range order is not destroyed by weak random fields in more than two dimensions if the order parameter has a discrete (e.g. Ising) symmetry. The characteristic interaction energy between the spins and the frozen-in defects increases as L Θ with the length scale L so that the static random-field-induced fluctuations dominate over the dynamic thermal fluctuations. Consequently, the critical behaviour is described by a T = 0 fixed point of the RNG transformation. This leads to pronounced non-classical critical exponents, a modified hyper-scaling v(d - Θ) = 2 – α and an activated critical dynamics. Domain wall roughening due to random fields produces metastability and hysteresis. The predicted logarithmic time dependence of the radius of the metastable mi-crodomains sets in after a characteristic time which depends on the details of the pinning mechanism and may exceed the age of the universe.