Lambda transition explained

The λ (lambda) universality class is a 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. While these systems are quite different at the first glance, they all are described by similar formalisms and their typical phase diagrams are identical.

See also

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

References

Books

• 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 Vol.1, edited by C. Gorter (North Holland, Amsterdam) 1955.

Journal articles

• Helfrich . W. . Defect model of the smectic A-nematic phase transition . Journal de Physique . EDP Sciences . 39 . 11 . 1978 . 0302-0738 . 10.1051/jphys:0197800390110119900 . 1199–1208. 617508 . 10.1.1.323.6028 .
• Nelson . David R. . Toner . John . Bond-orientational order, dislocation loops, and melting of solids and smectic-Aliquid crystals . Physical Review B . American Physical Society (APS) . 24 . 1 . 1 June 1981 . 0163-1829 . 10.1103/physrevb.24.363 . 363–387. 1981PhRvB..24..363N .
• Dasgupta . C. . Halperin . B. I. . Phase Transition in a Lattice Model of Superconductivity . Physical Review Letters . American Physical Society (APS) . 47 . 21 . 23 November 1981 . 0031-9007 . 10.1103/physrevlett.47.1556 . 1556–1560. 1981PhRvL..47.1556D .
• Williams . Gary A. . Vortex-ring model of the superfluidλtransition . Physical Review Letters . American Physical Society (APS) . 59 . 17 . 26 October 1987 . 0031-9007 . 10.1103/physrevlett.59.1926 . 1926–1929. 10035370 . 1987PhRvL..59.1926W .
• Onsager . L. . Statistical hydrodynamics . Il Nuovo Cimento . Springer Science and Business Media LLC . 6 . S2 . 1949 . 0029-6341 . 10.1007/bf02780991 . 279–287. 1949NCim....6S.279O . 186224016 .
• de Gennes . P.G. . An analogy between superconductors and smectics A . Solid State Communications . Elsevier BV . 10 . 9 . 1972 . 0038-1098 . 10.1016/0038-1098(72)90186-x . 753–756. 1972SSCom..10..753D .
• Abrikosov . A. A. . Zhurnal Éksperimental'noĭ i Teoreticheskoĭ Fiziki. 32. 6. 1957. 1442. ru. [unknown title]. Translated as: Abrikosov . A. A. . Soviet Physics JETP . 5. 6 . 1957 . 1174. On the Magnetic Properties of Superconductors of the Second Group.
• Renn . S. R. . Lubensky . T. C. . Abrikosov dislocation lattice in a model of the cholesteric–to–smectic-Atransition . Physical Review A . American Physical Society (APS) . 38 . 4 . 1 July 1988 . 0556-2791 . 10.1103/physreva.38.2132 . 9900613 . 2132–2147. 1988PhRvA..38.2132R .