In this paper we present a theoretical approach that allows us to describe the transition between critical and noncritical behavior when stocastic noise is introduced in extremal models with disorder. Namely, we show that the introduction of thermal noise in invasion percolation (IP) brings the system outside the critical point. This result suggests a possible definition of 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 IP and Eden models for $\overrightarrow{T}0$ and $\overrightarrow{T}\infty ,$ respectively. For small T we find a dynamical second-order transition with correlation length diverging when $\overrightarrow{T}0.$

• Received 26 August 1999

DOI:https://doi.org/10.1103/PhysRevE.62.7638