Critical behavior of slider-block model

This paper applies the theory of continuous phase transitions of statistical mechanics to a slider-block model. The slider-block model is chosen as a representative of systems with avalanches. Similar behavior can be observed in a forest-fire model and a sand-pile model. Basing on the well-developed theory of critical phenomena for percolating systems a strong analogy for the slider-block model is investigated. It is found that the slider-block model has a critical point when the stiffness of the model is infinite. Critical exponents are found and it is shown that the behavior of the slider-block model, particularly, the occurrence of system-wide events is strongly dominated by the finite-size effects. Also the unknown before behavior of the frequency-size distributions is found for large statistics of events.