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Abstract
Spin glasses and diluted magnetic semiconductors are both materials whose magnetic properties are strongly influenced by disorder. In spin glasses, the interplay of disorder and frustration in the interactions between spins leads to exceptionally slow spin relaxation and intrinsically non-equilibrium (aging) dynamics. A new approach to understanding the aging dynamics of short-range spin glass models is introduced here. It is shown that the dynamics have a symmetry under time reparametrizations, and the soft modes in the system are identified as spatially varying time reparametrizations. This leads to a number of predictions for the scaling properties of local quantities that are found to be in good agreement with numerical simulations. In diluted magnetic semiconductors, magnetic ions introduced into the host semiconductor have random positions. Monte Carlo simulations performed on an impurity band model for diluted magnetic semiconductors indicate that the positional disorder of the magnetic ions leads to an inhomogeneous ferromagnetic state. It is conjectured that many of the observed properties of diluted magnetic semiconductors can be understood using a two-component model, in which manganese spins are either strongly or weakly involved in the ferromagnetism depending on their local environment.
