We present both theoretical and numerical analyses of a cellular automaton
version of a slider-block model or threshold model that includes long-range
interactions. Theoretically we develop a coarse-grained description in the
mean-field (infinite range) limit and discuss the relevance of the metasta
ble state, limit of stability (spinodal), and nucleation to the phenomenolo
gy of the model. We also simulate the model and confirm the relevance of th
e theory for systems with long- but finite-range interactions. Results of p
articular interest include the existence of Gutenberg-Richter-like scaling
consistent with that found on real earthquake fault systems, the associatio
n of large events with nucleation near the spinodal, and the result that su
ch systems can be described, in the mean-field limit, with techniques appro
priate to systems in equilibrium. [S1063-651X(99)02908-6].