Spinodals, scaling, and ergodicity in a threshold model with long-range stress transfer

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].