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My favourite Nobel prize: a universal theory for phase transitions

24 Sep 2019 Hamish Johnston

With the 2019 Nobel Prize for Physics due to be announced on Tuesday 8 October, Physics World journalists pick their favourite Nobel awards from the past. Here Hamish Johnston argues the case for the 1982 prize for creating a complete and tractable theory of phase transitions

Different length scales: a phase transition in action. (Courtesy: iStock/hanohiki)

Phase transitions underpin much of physics – from the everyday freezing of liquid water to the esoteric symmetry-breaking that occurred in the very early universe.

Indeed, I think that many physicists view the world in terms of phase transitions – both real and metaphorical. The spontaneous stopping and starting of heavy traffic on a motorway looks like a phase transition to a physicist – and some physicists argue that it actually is one.

Kenneth Wilson

That is why my favourite Nobel prize was given in 1982 to Kenneth Wilson for “for his theory for critical phenomena in connection with phase transitions”.

Prior to Wilson’s work in the early 1970s, physicists had no successful general theory for how phase transitions occur – although they did know that very different systems (such as liquids and magnets) seemed to behave in similar ways.

Phase transitions were difficult to describe at a fundamental level because they involve fluctuations on many different length scales. When liquid water is chilled to the freezing point, for example, tiny pieces of ice just a few molecules in size will form and then disappear alongside millimetre and centimetre sized pieces. If the water is a large lake, kilometre-sized pieces of ice can coexist with similar sized regions of water.

A common strategy in physics is to work within a specific length scale, which often makes it easier do calculations. This does not work in the case of phase transitions because fluctuations at all length scales are important.

Wilson addressed this problem by adapting an existing framework called renormalization group theory, which allowed him to fold the physics at all relevant length scales into a manageable calculation. A profound result of this technique is that it revealed that the nature of a phase transition is defined by just two parameters: the dimensionality of the system (1D, 2D or 3D) and the dimensionality of a key quantity called the order parameter. This explained why very different physical systems underwent phase transitions in identical ways.

So, the next time you are driving along the motorway and traffic comes to a screeching halt, see if you can work out what the order parameter is – and thank Kenneth Wilson for giving you something to do while you are stuck in traffic.

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