Invasion Percolation with Temperature and the Nature of SOC in Real Systems

Andrea Gabrielli, Guido Caldarelli, Luciano Pietronero

Published 1999-10-26Version 1

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 SOC systems as ordinary critical systems where the critical point correspond to set to 0 one of the parameters. We recover both IP and EDEN model, for $T \to 0$, and $T \to \infty$ respectively. For small $T$ we find a dynamical second order transition with correlation length diverging when $T \to 0$.