The Physics of Complex Systems

Abstract

In the first section of this chapter, we summarize the basic concepts of critical behavior in thermodynamics, using the simplest spin system (Ising model) as illustration. In the second section, we discuss the geometric critical behavior obtained in the formation of clusters of diverging size (percolation).

Great fleas have little fleas

Upon their backs to bite ’em.

And little fleas have lesser fleas,

And so ad infinitum.

And the great fleas themselves, in turn,

Have greater fleas to go on,

While these again have greater still,

And greater still, and so on.

Augustus de Morgan (1801–1871)

(paraphrasing Jonathan Swift)