Lambda transition
Encyclopedia
The λ 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 crystal
s). All these systems are expected to belong to the same universality class for the thermodynamic critical properties of the phase transition.
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 defect
s.
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.
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.
Condensed matter physics
Condensed matter physics deals with the physical properties of condensed phases of matter. These properties appear when a number of atoms at the supramolecular and macromolecular scale interact strongly and adhere to each other or are otherwise highly concentrated in a system. The most familiar...
. It regroups several systems possessing strong analogies, namely, superfluids, superconductors and smectics (liquid crystal
Liquid crystal
Liquid crystals are a state of matter that have properties between those of a conventional liquid and those of a solid crystal. For instance, an LC may flow like a liquid, but its molecules may be oriented in a crystal-like way. There are many different types of LC phases, which can be...
s). All these systems are expected to belong to the same universality class for the thermodynamic critical properties of the phase transition.
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 modelXY model
The classical XY model is a model of statistical mechanics. It is the special case of the n-vector model for n=2.-Definition:...
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 defect
Topological defect
In mathematics and physics, a topological soliton or a topological defect is a solution of a system of partial differential equations or of a quantum field theory homotopically distinct from the vacuum solution; it can be proven to exist because the boundary conditions entail the existence of...
s.
In two dimensions (2D) the topological defects take the form of vortices and give rise to the
Kosterlitz-Thouless transition
Kosterlitz-Thouless transition
In statistical mechanics, a part of mathematical physics, the Kosterlitz–Thouless transition, or Berezinsky–Kosterlitz–Thouless transition, is a kind of phase transition that appears in the XY model in 2 spatial dimensions. The XY model is a 2-dimensional vector spin model that possesses U or...
. 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 ofdebate. 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
- SuperfluidSuperfluidSuperfluidity is a state of matter in which the matter behaves like a fluid without viscosity and with extremely high thermal conductivity. The substance, which appears to be a normal liquid, will flow without friction past any surface, which allows it to continue to circulate over obstructions and...
- Superconductor
- Liquid crystalLiquid crystalLiquid crystals are a state of matter that have properties between those of a conventional liquid and those of a solid crystal. For instance, an LC may flow like a liquid, but its molecules may be oriented in a crystal-like way. There are many different types of LC phases, which can be...
- Phase transitionPhase transitionA phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
- Renormalization groupRenormalization groupIn theoretical physics, the renormalization group refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales...
- Topological defectTopological defectIn mathematics and physics, a topological soliton or a topological defect is a solution of a system of partial differential equations or of a quantum field theory homotopically distinct from the vacuum solution; it can be proven to exist because the boundary conditions entail the existence of...
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.