WILSON & FISHER. Critical Exponents in 3.99 Dimensions, pp. 240-3 in Physical Review Letters Vol. 28, No. 4, January 24, 1972 [With:] WILSON. Feynman-Graph Expansion for Critical Exponents, pp. 548-51 in Physical Review Letters Vol. 28, No. 9, February 28, 1972

WILSON, K. G. & FISHER, M. E.

Date d'édition : 1972

A propos de cet article

First edition, complete journal issues. "Ken Wilson was one of a very small number of physicists who changed the way we all think, not just about specific phenomena, but about a vast range of different phenomena" (Steven Weinberg, New York Times Obituary). "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" (Nobel Prize press release). Several theories had been put forward but these had all failed to describe correctly the observed behaviour near the critical point. "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 . . . 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 . . . All these fluctuations are of importance near the critical point and a theoretical description must take into account the entire spectrum of fluctuations . . . 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. 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 . . . 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 . . . 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" (ibid.). Large 8vo, pp. 529-81; 199-260. Original printed wrappers (address label on rear wrappers, the January issue bumped near top of spine).

N° de réf. du vendeur ABE-1666955373345

Détails bibliographiques

• Titre: WILSON & FISHER. Critical Exponents in 3.99 Dimensions, pp. 240-3 in Physical Review Letters Vol. 28, No. 4, January 24, 1972 [With:] WILSON. Feynman-Graph Expansion for Critical Exponents, pp. 548-51 in Physical Review Letters Vol. 28, No. 9, February 28, 1972
• Date de parution: 1972
• Reliure: Soft cover
• Édition: 1st Edition
• État de l'article: Very Good