Invasion percolation with temperature and the nature of self-organized criticality in real systems

In this paper we present a theoretical approach that allows us to describe the transition between critical and noncritical behavior when stocastic noi se is introduced in extremal models with disorder. Namely, we show that the introduction of thermal noise in invasion percolation (IP) brings the syst em outside;the critical point. This result suggests a possible definition o f self-organized criticality systems as ordinary critical systems where the critical. point corresponds to set to 0 one of the parameters. We recover both the TP and Eden models for T-->0 and T-->infinity, respectively. For s mall T we fmd a dynamical second-order transition with correlation length d iverging when T-->0.