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INTRODUCTION


Background

(See references)


Lambda (λ) transition universality class



While these systems are quite different at the first glance, they all are discribed by similar formalisms and their typical Phase Diagrams are identical.


THEORY OF THE λ TRANSITION

Systems falling into this universality class can be characterized by a complex order parameter. Theories to unify these phenonenons 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 MICROSCOPIC ORIGIN OF λ TRANSITION : TOPOLOGICAL MELTING ?

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.


SEE ALSO



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 editedby C. Gorter Vol.1 (North Holland,Amsterdam) 1955.



Journal articles


  • 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.