We study a class of stochastic Ising (or interacting particle) systems
that exhibit a spatial distribution of impurities that change with ti
me. it may model, for instance, steady nonequilibrium conditions of th
e kind that may be induced by diffusion in some disordered materials.
Different assumptions for the degree of coupling between the spin and
the impurity configurations are considered. Two interesting well-defin
ed limits for impurities that behave autonomously are (i) the standard
(i.e., quenched) bond-diluted, random-field, random-exchange, and spi
n-glass Ising models, and (ii) kinetic variations of these standard ca
ses in which conflicting kinetics simulate fast and random diffusion o
f impurities. A generalization of the Mattis model with disorder that
describes a crossover from the equilibrium case (i) to the nonequilibr
ium case (ii) and the microscopic structure of a generalized heat bath
are explicitly worked out as specific realizations of our class of mo
dels. We sketch a simple classification of transition rates for the ti
me evolution of the spin configuration based on the critical behavior
that is exhibited by the models in case (ii). The latter are shown to
have an exact solution for any lattice dimension for some special choi
ce of rates.