Scale invariance and universality: organizing principles in complex systems

This paper is a brief summary of a talk that was designed to address the qu estion of whether two of the pillars of the field of phase transitions and critical phenomena - scale invariance and universally - can be useful in gu iding research on a broad class of complex phenomena. We shall see that whi le scale invariance has been tested for many years, universality is relativ ely more rarely discussed. In particular, we shall develop a heuristic argu ment that serves to make more plausible the universality hypothesis in both thermal critical phenomena and percolation phenomena, and suggest that thi s argument could be developed into a possible coherent approach to understa nding the ubiquity of scale invariance and universality in a wide range of complex systems. (C) 2000 Elsevier Science B.V. All rights reserved.