# Award ceremony speech

Presentation Speech by Professor Stig Lundqvist of the Royal Academy of Sciences

Translation from the Swedish text

Your Majesties, Your Royal Highnesses, Ladies and Gentlemen,

The development in physics is on the whole characterized by a close interaction between experiment and theory. New experimental discoveries lead often rapidly to the development of theoretical ideas and methods that predict new phenomena and thereby stimulate further important experimental progress. This close interaction between theory and experiment keeps the frontiers of physics moving forward very rapidly.

However, there have been a few important exceptions, where the experimental facts have been well known for a long time but where the fundamental theoretical understanding has been lacking and where the early theoretical models have been incomplete or even seriously in error. I mention here three classical examples from the physics of the twentieth century, namely superconductivity, critical phenomena and turbulence. Superconductivity was discovered in the beginning of this century, but in spite of great theoretical efforts by many famous physicists, it took about fifty years until a satisfactory theory was developed. The theory of superconductivity was awarded the Nobel Prize in physics exactly ten years ago. The critical phenomena occur at phase transitions, for example between liquid and gas. These phenomena were known even before the turn of the century, and some simple but incomplete theoretical models were developed at an early stage. In spite of considerable theoretical efforts over many decades, one had to wait until the early seventies for the solution. The problem was solved in an elegant and profound way by Kenneth Wilson, who developed the theory which has been awarded this year’s Nobel Prize in physics. The third classical problem I mentioned, namely turbulence, has not yet been solved, and remains a challenge for the theoretical physicists.

From daily life we know that matter can exist in different phases and that transitions from one phase to another may occur if we change, for example, the temperature. A liquid goes over into gas phase when sufficiently heated, a metal melts at a certain temperature, a permanent magnet loses its magnetization above a certain critical temperature, just to give a few examples. Let us consider the transition between liquid and gas. When we come close to the critical point, there will appear fluctuations in the density of the liquid at all possible scales. These fluctuations take the forms of drops of liquids mixed with bubbles of gas. There will be drops and bubbles of all sizes from the size of a single molecule to the volume of the system. Exactly at the critical point the scale of the largest fluctuations becomes infinite, but the role of the smaller fluctuations can by no means be ignored. A proper theory for the critical phenomena must take into account the entire spectrum of length scales. In most problems in physics one has to deal with only one length scale. This problem required the development of a new type of theory capable of describing phenomena at all possible length scales, for example, from the order of a centimeter down to less than one millionth of a centimeter.

Wilson succeeded in an ingenious way to develop a method to solve the problem, published in two papers from 1971. A frontal attack on this problem is impossible, but he found a method to divide the problem into a sequence of simpler problems, in which each part can be solved. Wilson built his theory on an essential modification of a method in theoretical physics called renormalization group theory.

Wilson’s theory gave a complete theoretical description of the behaviour close to the critical point and gave also methods to calculate numerically the crucial quantities. During the decade since he published his first papers we have seen a complete breakthrough of his ideas and methods. The Wilson theory is now also successfully applied to a variety of problems in other areas of physics.

Professor Wilson,

You are the first theoretical physicist to develop a general and tractable method, where widely different scales of length appear simultaneously. Your theory has given a complete solution to the classical problem of critical phenomena at phase transitions. Your new ideas and methods seem also to have a great potential to attack other important and up to now unsolved problems in physics.

I am very happy to have the privilege of expressing the warmest congratulations of the Royal Swedish Academy of Sciences. I now ask you to receive your Nobel Prize from the hands of His Majesty the King.

### Nobel Prizes and laureates

See them all presented here.