H. Ceva et Rpj. Perazzo, FROM SELF-ORGANIZED CRITICALITY TO 1ST-ORDER-LIKE BEHAVIOR - A NEW-TYPE OF PERCOLATIVE TRANSITION, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 48(1), 1993, pp. 157-160
A modification of one of the standard models of avalanches in a sandpi
le is proposed. We allow two different values of the critical slope: a
sliding never starts with a slope below the upper value and stops onl
y when the local slope falls below the lower one. As a result we find
that the only avalanches present involve the whole system, in sharp co
ntrast with what is expected from self-organized critical models. This
behavior resembles more a first-order transition than a second-order
one. We present a method to study the gradual change from one behavior
to the other. A possible link with percolative transitions is discuss
ed.