The Ising model, computer simulation, and universal physics

Abstract

So the crucial change of emphasis of the last twenty or thirty years that distinguishes the new era from the old one is that when we look at the theory of condensed matter nowadays we inevitably talk about a ‘model.’ Michael Fisher (1983, 47) It is a curious fact that the index of The New Physics (Davies 1989), an anthology of eighteen substantial essays on recent developments in physics, contains only one entry on the topics of computers and computer simulation. Curious, because the computer is an indispensable tool in contemporary research. To different degrees, its advent has changed not just the way individual problems are addressed but also the sort of enterprise in which theorists engage, and hence the kind of theory that they propose. Consider, for example, chaos theory. Although the ideas underlying the theory were first explored by Poincar at the turn of the century, their development had to await the arrival of the computer. In The New Physics the beautiful pictures of fractal structures that illustrate the essay on chaos theory (Ford 1989) are, of course, computer generated. Yet, perhaps because it runs counter to the mythology of theoretical practice, that fact is mentioned neither in the captions that accompany the pictures nor elsewhere in the text. The indispensable has become invisible. The solitary entry on computers in the index takes us to the essay, ‘Critical Point Phenomena: Universal Physics at Large Length Scales’, by Alastair Bruce and David Wallace, and, within that essay, to a description of the so-called Ising model and the computer simulation of its behaviour.