  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.
