Lambda transition

Information about Lambda transition

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.

Introduction

Background

(See references)

Lambda (λ) transition universality class

While these systems are quite different at the first glance, they all are described 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 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 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 Vol.1, edited by C. Gorter (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.
Condensed matter physics is the field of physics that deals with the macroscopic physical properties of matter. In particular, it is concerned with the "condensed" phases that appear whenever the number of constituents in a system is extremely large and the interactions
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Superfluidity is a phase of matter or description of heat capacity in which "unusual" effects are observed when liquids, typically of helium-4 or helium-3, overcome friction by surface interaction when at a stage, known as the "lambda point" for helium-4, at which the liquid's
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Superconductivity is a phenomenon occurring in certain materials at extremely low temperatures, characterized by exactly zero electrical resistance and the exclusion of the interior magnetic field (the Meissner effect).
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Liquid crystals are substances that exhibit a phase of matter that has properties between those of a conventional liquid, and those of a solid crystal. For instance, a liquid crystal (LC) may flow like a liquid, but have the molecules in the liquid arranged and/or oriented in a
..... Click the link for more information.
Liquid crystals are substances that exhibit a phase of matter that has properties between those of a conventional liquid, and those of a solid crystal. For instance, a liquid crystal (LC) may flow like a liquid, but have the molecules in the liquid arranged and/or oriented in a
..... Click the link for more information.
In physical chemistry, mineralogy, and materials science, a phase diagram is a type of graph used to show the equilibrium conditions between the thermodynamically-distinct phases.
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Like the famous Ising and Heisenberg models, the XY model is one of the many highly simplified models in the branch of physics known as statistical mechanics. It is a special case of the n-vector model. In the XY model, 2D classical spins are confined to some lattice.
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The Kosterlitz-Thouless transition, or Berezinsky-Kosterlitz-Thouless transition, is a special transition seen in the XY model for interacting spin systems in 2 spatial dimensions. The XY model is a 2-Dimensional vector spin model that possesses U(1) or circular symmetry.
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Superfluidity is a phase of matter or description of heat capacity in which "unusual" effects are observed when liquids, typically of helium-4 or helium-3, overcome friction by surface interaction when at a stage, known as the "lambda point" for helium-4, at which the liquid's
..... Click the link for more information.
Superconductivity is a phenomenon occurring in certain materials at extremely low temperatures, characterized by exactly zero electrical resistance and the exclusion of the interior magnetic field (the Meissner effect).
..... Click the link for more information.
Liquid crystals are substances that exhibit a phase of matter that has properties between those of a conventional liquid, and those of a solid crystal. For instance, a liquid crystal (LC) may flow like a liquid, but have the molecules in the liquid arranged and/or oriented in a
..... Click the link for more information.
phase transition or phase change is the transformation of a thermodynamic system from one phase to another. The distinguishing characteristic of a phase transition is an abrupt change in one or more physical properties, in particular the heat capacity, with a small change in
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In theoretical physics, renormalization group (RG) refers to a mathematical apparatus that allows one to investigate the changes of a physical system as one views it at different distance scales.
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topological soliton or a topological defect is a solution of a system of partial differential equations or of a quantum field theory that can be proven to exist because the boundary conditions entail the existence of homotopically distinct solutions.
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