Mean field theory for ordinary and hot sandpiles

A mean eld theory is discussed for a sandpile model, a cellular automaton prototype of systems showing self-organized criticality. The previous formulation of the mean eld does not take into account the dissipation eects that take place on boundaries. This gives rise to some inconsistencies that are eliminated by carefully considering the boundaries eects, as it is shown in this paper. We present here a revised version of the MF equations. The main result is that criticality arises in the thermodynamic limit for sandpile systems, conrming numerical observations on the behavior of the order parameter. The mean eld approach is also generalized by applying it to the more general case of sandpiles in thermal equilibrium where a temperature-like parameter T is introduced. In this case we show that criticality is not destroyed at T > 0