The Theoretical Practices of Physics by Hughes R. I. G

Author:Hughes, R. I. G. [Hughes, R. I. G.]
Language: ru
Format: mobi
Publisher: OUP Oxford
Published: 2010-03-17T20:00:00+00:00

Fig. 5.4. Hierarchies of representation on the DDI account of modelling.

6

The Ising Model, Computer Simulation, and Universal Physics

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 Fisher1

PREAMBLE

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 merely the way individual problems are addressed, but the sort of enterprise in which theorists engage. Consider, for example, chaos theory. Although the ideas underlying the theory were first explored by Poincaré at the turn of the century, their development had to await the arrival of the computer.2 In The New Physics, the striking 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. The model is at the same time very simple and very remarkable. It is used to gain insight into phenomena associated with a diverse group of physical systems—so diverse, in fact, that the branch of physics that explores what is common to them all is called ‘universal physics’.

This essay has two sections. In section 6.1, I set out the relations between the phenomena, the Ising model, and the general theory of critical–point behaviour, and then outline the role played by computer simulations of the Ising model’s behaviour. In section 6.2, I show how the Ising model in particular, and computer simulations in general, can be accommodated within a philosophical account of theoretical representation.

6.1. CRITICAL–POINT PHENOMENA AND THE ISING

MODEL

6.1.1. The Phenomena

Various apparently dissimilar physical systems—magnets, liquids, binary alloys—exhibit radical changes in their properties at some critical temperature.

(a) Above the Curie temperature, TC (770°C), a specimen of iron will exhibit paramagnetic rather than ferromagnetic behaviour; that is to say, above TC it can be only feebly magnetized, below TC its magnetic susceptibility is very high.3

(b) At the boiling point of H2O, two phases, liquid and vapour, can coexist. The boiling point increases smoothly with pressure until the critical point is reached (pC = 218 atmospheres, TC = 374°C). At this point, the two phases cannot be distinguished; to quote Thomas Andrews, lecturing on similar behaviour in CO2at this point: ‘If anyone should ask whether it is now in the gaseous or liquid state, the question does not, I believe, admit of a positive reply.

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