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 metastable state, limit of stability (spinodal), and nucleation to the phenomenology of the model. We also simulate the model and confirm the relevance of the theory for systems with long- but finite-range interactions. Results of particular interest include the existence of Gutenberg-Richter-like scaling consistent with that found on real earthquake fault systems, the association of large events with nucleation near the spinodal, and the result that such systems can be described, in the mean-field limit, with techniques appropriate to systems in equilibrium.