Scaling and phase transitions in random systems

The effects of randomness on the nature of ordering and phase transitions in magnetic systems will be discussed. A brief review as well as new results on the role of randomness (random exchange, random axis anisotropy, and random field) in determining the properties of spin systems (Ising, Potts, XY and Heisenberg) will be presented. Our results are applicable to phase transitions in porous media, the vortex glass phase in oxide superconductors, and conductance noise in mesoscopic spin glasses. Mean field theory, T = 0 scaling, transfer matrix, and approximate renormalization group techniques have been used to obtain our results.