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

TL;DR

This paper investigates how thermal noise affects invasion percolation, revealing a connection to self-organized criticality and identifying a dynamical phase transition as temperature approaches zero.

Contribution

It introduces a framework linking thermal noise to criticality in invasion percolation, unifying models like IP and Eden through temperature limits.

Findings

Thermal noise shifts the system outside the critical point.

A second order transition occurs at low temperatures with diverging correlation length.

IP and Eden models are recovered at temperature extremes.

Abstract

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 $T \to 0$.