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The λ (lambda) universality class is probably the most important group in condensed matter physics. It regroups several systems possessing strong analogies, namely, superfluids, superconductors and smectics (liquid crystals). All these systems are expected to belong to the same universality class for the thermodynamic critical properties of the phase transition.

Contents 1 Introduction 1.1 Background 1.2 Lambda (λ) transition universality class 2 Theory of the λ transition 3 The microscopic origin of λ transition : topological melting ? 4 See also 5 References 5.1 Books 5.2 Journal articles

(See references)

While these systems are quite different at the first glance, they all are described by similar formalisms and their typical phase diagrams are identical.

Systems falling into this universality class can be characterized by a complex order parameter. Theories to unify these phenomena state that the XY model can be viewed as a discretized version of this type of systems.

An interesting feature of these models is the presence of thermally generated topological defects. In two dimensions (2D) the topological defects take the form of vortices and give rise to the Kosterlitz-Thouless transition. Also in 3D thermally generated vortex loops are present at the transition and it has been argued that the critical properties, both the static and the dynamic, can be associated with these vortex loops.

The role of topological excitations (defects) in driving phase transitions has long been a matter of debate. These topological excitations are borne by vortex (superfluids), magnetic flux (superconductors),and screw-dislocation (smectics) lines. The underlying microscopic mechanisms have been discussed theoretically by several authors and, as pointed out by most of them, analogous transitions should be driven by analogous mechanisms. In the absence of any applied external field, the common description of topological melting implies the appearance of finite-size line pairs in the ordered state, followed by the unbinding of these pairs at the order-disorder transition. The unbinding of the line pairs is described as the divergence of the defect size. In the presence of an external field, the order-disorder transition is expected to occur in, respectively,one or two steps according to whether the system is of type I or II. For type-II systems,an intermediate state exists with self-organised,unbound lines. Intermediate phases have been predicted and experimentally identified in either superfluids, superconductors or thermotropic smectics.

• Superfluid
• Superconductor
• Liquid crystal
• Phase transition
• Renormalization group
• Topological defect

• Chaikin P. M. and Lubensky T. C. Principles of Condensed Matter Physics (Cambridge

University Press,Cambridge) 1995, sect.9.

• Feynman R. P. Progress in Low Temperature Physics editedby C. Gorter Vol.1 (North Holland,Amsterdam) 1955.

• Helfrich W. J. Phys. (Paris) 39 (1978) 1199.

• Nelson D. R. and Toner J. Phys. Rev. B 24 (1981) 363.

• Dagupta C. and Halperin B. I. Phys. Rev. Lett.47 (1981) 1556.

• Williams G. A. Phys. Rev. Lett. 59 (1987) 1926.

• Onsager L. Nuovo Cimento Suppl. 6 (1949) 279.

• de Gennes P.-G. Sol. State Commun. 10 (1972) 753.

• Abrikosov A. A. Zh. Eksp. Teor. Fiz. 32 (1957) 1442.

• Abrikosov A. A. Sov. Phys. JETP 5 (1957) 1174.

• Renn S. and Lubensky T. C. Phys. Rev. A 38 (1988) 2132.