In statistical mechanics, universality is the observation that there are properties for a large class of systems that are independent of the dynamical details of the system. Systems display universality in a scaling limit, when a large number of interacting parts come together. The modern meaning of the term was introduced by Leo Kadanoff in the 1960s, but a simpler version of the concept was already implicit in the van der Waals equation and in the earlier Landau theory of phase transitions, which did not incorporate scaling correctly.
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| - Universalität (Physik) (de)
- Universality (dynamical systems) (en)
- 普遍性 (物理学) (zh)
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| - Das Konzept der Universalität wird in der statistischen Mechanik verwendet im Kontext der kontinuierlichen Phasenübergänge und der kritischen Phänomene. Universalität bezeichnet hier die Tatsache, dass gewisse Eigenschaften von Klassen von Systemen nur von wenigen Systemdetails abhängen: Vertreter einer Universalitätsklasse zeigen quantitativ dasselbe Verhalten (identische universelle Größen), obwohl sie ein anderes Kristallgitter, andere Wechselwirkungen und andere Unterschiede aufweisen. (de)
- 在物理学中，普遍性（universality）说很多系统有相似的大规模数字属性，不依赖系统的小细节，例如临界指数。常见的是，系统在缩放极限表示普遍性。普遍性这个观念在动力学和其他数学分支中有庞大的应用。普遍性源于物理学中的统计力学和量子场论。 (zh)
- In statistical mechanics, universality is the observation that there are properties for a large class of systems that are independent of the dynamical details of the system. Systems display universality in a scaling limit, when a large number of interacting parts come together. The modern meaning of the term was introduced by Leo Kadanoff in the 1960s, but a simpler version of the concept was already implicit in the van der Waals equation and in the earlier Landau theory of phase transitions, which did not incorporate scaling correctly. (en)
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| - Das Konzept der Universalität wird in der statistischen Mechanik verwendet im Kontext der kontinuierlichen Phasenübergänge und der kritischen Phänomene. Universalität bezeichnet hier die Tatsache, dass gewisse Eigenschaften von Klassen von Systemen nur von wenigen Systemdetails abhängen: Vertreter einer Universalitätsklasse zeigen quantitativ dasselbe Verhalten (identische universelle Größen), obwohl sie ein anderes Kristallgitter, andere Wechselwirkungen und andere Unterschiede aufweisen. (de)
- In statistical mechanics, universality is the observation that there are properties for a large class of systems that are independent of the dynamical details of the system. Systems display universality in a scaling limit, when a large number of interacting parts come together. The modern meaning of the term was introduced by Leo Kadanoff in the 1960s, but a simpler version of the concept was already implicit in the van der Waals equation and in the earlier Landau theory of phase transitions, which did not incorporate scaling correctly. The term is slowly gaining a broader usage in several fields of mathematics, including combinatorics and probability theory, whenever the quantitative features of a structure (such as asymptotic behaviour) can be deduced from a few global parameters appearing in the definition, without requiring knowledge of the details of the system. The renormalization group provides an intuitively appealing, albeit mathematically non-rigorous, explanation of universality. It classifies operators in a statistical field theory into relevant and irrelevant. Relevant operators are those responsible for perturbations to the free energy, the , that will affect the continuum limit, and can be seen at long distances. Irrelevant operators are those that only change the short-distance details. The collection of scale-invariant statistical theories define the universality classes, and the finite-dimensional list of coefficients of relevant operators parametrize the near-critical behavior. (en)
- 在物理学中，普遍性（universality）说很多系统有相似的大规模数字属性，不依赖系统的小细节，例如临界指数。常见的是，系统在缩放极限表示普遍性。普遍性这个观念在动力学和其他数学分支中有庞大的应用。普遍性源于物理学中的统计力学和量子场论。 (zh)
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