18 October 1982

**NEW THEORY FOR PHASE TRANSITIONS
AWARDED**

The Royal Swedish
Academy of Sciences has decided to award the Nobel Prize in
Physics for 1982 to

Professor **Kenneth G. Wilson**, Cornell University,
Ithaca, USA **for his theory for critical phenomena in
connection with phase transitions.**

In daily life and from classical physics 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 pressure or the
temperature. A liquid goes over into a 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.

Phase transitions have been studied in physics over a long time
and for a large number of different systems. The phase transition
is often characterized by an abrupt change in the value of some
physical properties. In other cases the transition from one phase
to another may be rather smooth. Examples of the latter case is
the transition between liquid and gas at the critical point, and
from ferromagnetism to paramagnetism in metals such as iron,
nickel and cobalt. These smooth phase transitions show instead a
number of typical anomalies near the critical point. Some
quantities grow above all limits when one approaches the critical
temperature. These anomalies, usually called *critical
phenomena*, have to do with the very large fluctuations that
occur in the system when we come close to the critical
point.

A first qualitative description of the critical behaviour of some
special al systems was given already around the turn of the
century. Examples are the transition between liquid and gas and
the transition between ferromagnetism and paramagnetism. The
Soviet physicist L. Landau (Nobel
Laureate in Physics 1962) published in 1937 a general theory
for phase transitions, which contained the results of most
earlier theories as special cases.

An essential step towards a further understanding was taken when
L. Onsager (Nobel
Laureate in Chemistry 1968) found the exact solution for the
thermodynamic properties of a twodimensional model, that had been
frequently discussed. It was a great surprise to find that the
theory of Landau as well as all previous theories failed
completely in predicting the behaviour close to the critical
point. This puzzling result led to extensive and detailed studies
of a large number of systems, and one found that the critical
behaviour was quite different from the predictions by the Landau
theory. Numerical calculations using different theoretical models
also showed strong deviations from the Landau theory. M.E.
Fisher, Cornell University played a leading role through his
analysis of experimental data, supported by theoretical analysis
and numerical calculations and, probably most important; by
taking initiative and acting as a catalyst for further progress.
One should mention important theoretical contributions by B.
Widom, also at Cornell University, by the Soviet physcists
*A.Z. Patashinskii* and *V.L. Pokrovski* and, most
important by *L.P. Kadanoff*, University of
Chicago. Kadanoff put forward a very important new and
original idea which seemed to have strong influence on the later
development. His theory, however, did not make it possible to
calculate the critical behaviour.

The problem was solved in a definite and profound way by
**Kenneth Wilson** in two fundamental papers from 1971 and
followed by a series of papers in the following years. Wilson
realized that the critical phenomena are different from most
other phenomena in physics in that one has to deal with
fluctuations in the system. over widely different scales of
length. We have normally to do with only one given scale of
length for any given phenomenon. Examples of the normal situation
is the physics of radio waves, hydrodynamic waves, visible light
, atoms, nuclei, elementary particles where each system is
characterized by a certain scale of length and we do not have to
be concerned with widely different scales of length. For a
condensed system or gas near the critical point, however, we
cannot limit ourselves to one single scale of length. Besides the
large-scale fluctuations of the same order of size as the entire
system. We have fluctuations of shorter range all the way down to
atomic dimension. In typical cases we may have fluctuations with
a range of the order of centimetre and all the way down to less
than one millionth of a centimetre. All these fluctuations are of
importance near the critical point and a theoretical description
must take into account the entire spectrum of fluctuations. A
frontal attack with direct methods is out of the question even
with the assistance of the fastest computers.

Wilson succeeded in an ingenious way to develop a method to solve
the problem. instead of a frontal attack, he developed 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*, which was developed already
during the fifties and was applied with varying success to
different problems.

Wilson's theory for critical phenomena gave a complete
theoretical description of the behaviour close to the critical
point and gave also methods to calculate numerically the crucial
quantities. His analysis showed that sufficiently close to the
critical point most of the variables of the system become
redundant. The critical phenomena are essentially determined by
two numbers: the dimensionality of the system (1, 2 or 3) and the
dimensionality of a key quantity called the *order
parameter*, a quantity introduced already in Landau's theory.
This is a physical result of great generality. It implies that
many systems, different and completely unrelated, can show
identical behaviour near the critical point. As examples we can
mention that liquids, mixtures of liquids, ferromagnets, and
binary alloys show the same critical behaviour. Experimental and
theoretical work from the sixties suggested this form of
universality, but Wilson's theory gave a convincing proof from
fundamental principles. Calculations of the crucial parameters
show consistently good agreement with experimental data.

Wilson is the first physicist to develop a general and tractable
method where widely different scales of lengths appear
simultaneously. The method is therefore, with proper
modifications, applicable also to some other important and yet
unsolved problems. Turbulence in fluids and gases is a classical
example, where many different scales of length occur. In the
atmosphere we find turbulent flow of all sized from the tiniest
whirl of dust to hurricanes. Wilson's new ideas have also found
application within particle physics. He has developed a modified
form of the theory and successfully applied it to current
problems in particle physics, particularly quark confinement.
Wilson's theoretical methods represent a new form of theory which
has given a complete solution to the classical problem of
critical phenomena at phase transitions but which also seems to
have a great potential to attack other important and up to now
unsolved problems.

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