Generating nonequilibrium steady states by conflicting dynamics, i.e., superposition of spin flip processes in Ising-like systems has a precedent in the consideration of spatially nonuniform distributions of temperature (Garrido & Marro 1987). It was introduced as a drastic simplification of more complex practical situations such as systems with different temperatures at opposing boundaries (Creutz 1986, Harris & Grant 1988). This has in turn suggested studying spins that suffer competing action of several baths, e.g., two independent thermal baths with respective probabilities p and 1 — p, and the case in which different sites of the lattice, either a sublattice or else a set of sites chosen at random, are at different temperatures. After some effort, it appears that these systems involving several temperatures probably have the critical behavior that characterizes the original system from which they derive, at least when all the involved temperatures are finite, and no essential symmetry is broken. In spite of such apparent simplicity, phase diagrams and other thermodynamic properties are varied and interesting, and some questions remain unresolved.

Our concern in this chapter is a class of closely related systems that are less well understood. We discuss a (rather arbitrary) selection of stochastic, interacting particle systems of the kind introduced in chapter 7, namely, a nonequilibrium Ising glass (§8.1 and §8.2), and the cases of bond dilution and very strong bonds (§8.1), invasion and voting processes (§8.3), and kinetic versions of systems in which interactions extend beyond nearest neighbors (§8.4).