Dual Description of the Superconducting Phase Transition

Kiometzis, Michael; Kleinert, H.; Schakel, Adriaan M. J.

doi:10.1002/prop.2190430803

Cited by 55 publications

(68 citation statements)

References 40 publications

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“…This has been confirmed by Monte Carlo (MC) simulations of the lattice model [6], with the critical value κ c = (0.76 ± 0.04)/ √ 2 [7]. Duality arguments indicate that the system belongs to the same universality class as of the three-dimensional XY-model [8][9][10].…”

Section: Introductionmentioning

confidence: 63%

Fixed point structure of the Abelian Higgs model

Fejős

Hatsuda

2016

Phys. Rev. D

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The order of the superconducting phase transition is analyzed via the functional renormalization group approach. For the first time, we derive fully analytic expressions for the β functions of the charge and the self-coupling in the Abelian Higgs model with one complex scalar field in d = 3 dimensions that support the existence of two charged fixed points: an infrared (IR) stable fixed point describing a second-order phase transition and a tritical fixed point controlling the region of the parameter space that is attracted by the former one. It is found that the region separating firstand second-order transitions can be uniquely characterized by the Ginzburg-Landau parameter κ, and the system undergoes a second order transition, only if κ > κc ≈ 0.62/ √ 2.

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Section: Introductionmentioning

confidence: 63%

Fixed point structure of the Abelian Higgs model

Fejős

Hatsuda

2016

Phys. Rev. D

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“…1,2,3,4,5 This means that the superconducting phase maps onto the symmetric phase, and the normal phase onto the broken phase. Furthermore, the dual counterpart of the order parameter of the XY model is a non-perturbative field that creates the Abrikosov-Nielsen-Olesen vortices in the superconductor.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of duality and universality in a frozen superconductor

Neuhaus¹,

Rajantie

Rummukainen

2003

Phys. Rev. B

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The three-dimensional integer-valued lattice gauge theory, which is also known as a "frozen superconductor," can be obtained as a certain limit of the Ginzburg-Landau theory of superconductivity, and is believed to be in the same universality class. It is also exactly dual to the three-dimensional XY model. We use this duality to demonstrate the practicality of recently developed methods for studying topological defects, and investigate the critical behaviour of the phase transition using numerical Monte Carlo simulations of both theories. On the gauge theory side, we concentrate on the vortex tension and the penetration depth, which map onto the correlation lengths of the order parameter and the Noether current in the XY model, respectively. We show how these quantities behave near the critical point, and that the penetration depth exhibits critical scaling only very close to the transition point. This may explain the failure of superconductor experiments to see the inverted XY model scaling.

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“…It turns out that, performing the summation over this grand canonical ensemble by imposing the property of a short-range repulsion of monopole loops, one obtains an effective description of the monopole condensate in terms of a magnetically charged Higgs field [114,115]. Accordingly, the resulting mean field theory is a dual Abelian Higgs model, in which the dual Higgs field minimally interacts with the dual gauge field.…”

Section: String Representation Of the 'T Hooft-loop Average In The [Umentioning

confidence: 99%

“…One further imposes the summation over the grand canonical ensemble of monopole loops in the form of the average of the phase factor in Equation (74) with the following path-integral measure [114,115]:…”

Section: String Representation Of the 'T Hooft-loop Average In The [Umentioning

confidence: 99%

Monopole-Based Scenarios of Confinement and Deconfinement in 3D and 4D

Bellettre

2017

Universe

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This review discusses confinement, as well as the topological and critical phenomena, in the gauge theories which provide the condensation of magnetic monopoles. These theories include the 3D SU(N ) Georgi-Glashow model, the 4D [U(1)] N −1 -invariant compact QED , and the [U(1)] N −1 -invariant dual Abelian Higgs model. After a general introduction to the string models of confinement, an analytic description of this penomenon is provided at the example of the 3D SU(N ) Georgi-Glashow model, with a special emphasis placed on the so-called Casimir scaling of k-string tensions in that model. We further discuss the string representation of the 3D [U(1)] N −1 -invariant compact QED, as well as of its 4D generalization with the inclusion of the Θ-term. We compare topological effects, which appear in the latter case, with those that take place in the 3D QED extended by the Chern-Simons term. We further discuss the string representation of the 't Hooft-loop average in the [U(1)] N −1 -invariant dual Abelian Higgs model extended by the Θ-term, along with the topological effects caused by this term. These topological effects are compared with those occurring in the 3D dual Abelian Higgs model (i.e., the dual Landau-Ginzburg theory) extended by the Chern-Simons term. In the second part of the review, we discuss critical properties of the weakly-coupled 3D confining theories. These theories include the 3D compact QED, along with its fermionic extension, and the 3D Georgi-Glashow model. Keywords: magnetic monopoles; Abelian-type models of confinement; string representation of the Wilson-and the 't Hooft-loop averages; Aharonov-Bohm and other topological effects; Casimir scaling of k-string tensions; critical properties of the 3D weakly coupled confining theories Topological Effects in the Abelian-Type Confining Theories IntroductionIn this review, we discuss various non-perturbative phenomena that take place in the Abelian-type confining gauge theories. We start this discussion with recalling some basic facts about confinement, the large-distance static quark-antiquark potential associated with it, and the related models of the confining string. As is well known, because of confinement in QCD, quarks and gluons do not exist as individual particles, but appear only in the form of bound states (for recent reviews, see [1][2][3]). The latter include mesons, baryons, glueballs, and the so-called hybrids consisting of a quark, an antiquark, and one or several gluons. Confining interactions that take place between the constituents of the bound states, can occur through string-like Euclidean configurations of the Yang-Mills field. Such effective strings can be viewed as the microscopic tubes that carry fluxes of the gauge field from one constituent to another, which is the reason for calling them "the QCD flux tubes" [4][5][6][7]. Similar flux tubes, called Abrikosov vortices [8,9] (for a relativistic generalization, see [10]), exist in type-II superconductors, in which case they represent stable cylindrically-symmetric s...

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Dual Description of the Superconducting Phase Transition

Cited by 55 publications

References 40 publications

Fixed point structure of the Abelian Higgs model

Fixed point structure of the Abelian Higgs model

Numerical study of duality and universality in a frozen superconductor

Monopole-Based Scenarios of Confinement and Deconfinement in 3D and 4D

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