41 research outputs found
Gauge-invariant critical exponents for the Ginzburg-Landau model
The critical behavior of the Ginzburg-Landau model is described in a
manifestly gauge-invariant manner. The gauge-invariant correlation-function
exponent is computed to first order in the and -expansion, and found
to agree with the ordinary exponent obtained in the covariant gauge, with the
parameter in the gauge-fixing term .Comment: 4 pages, no figure
Critical Behavior of the Meissner Transition in the Lattice London Superconductor
We carry out Monte Carlo simulations of the three dimensional (3D) lattice
London superconductor in zero applied magnetic field, making a detailed finite
size scaling analysis of the Meissner transition. We find that the magnetic
penetration length \lambda, and the correlation length \xi, scale as \lambda ~
\xi ~ |t|^{-\nu}, with \nu = 0.66 \pm 0.03, consistent with ordinary 3D XY
universality, \nu_XY ~ 2/3. Our results confirm the anomalous scaling dimension
of magnetic field correlations at T_c.Comment: 4 pages, 5 ps figure
Critical Exponents of the Superconducting Phase Transition
We study the critical exponents of the superconducting phase transition in
the context of renormalization group theory starting from a dual formulation of
the Ginzburg-Landau theory. The dual formulation describes a loop gas of
Abrikosov flux tubes which proliferate when the critical temperature is
approached from below. In contrast to the Ginzburg-Landau theory, it has a
spontaneously broken global symmetry and possesses an infrared stable fixed
point. The exponents coincide with those of a superfluid with reversed
temperature axis.Comment: Postscript file. For related work see www adress
http://www.physik.fu-berlin.de/kleiner_re.html in our homepage
http://www.physik.fu-berlin.de/kleinert.htm
Critical behavior of Ginzburg-Landau model coupled to massless Dirac fermions
We point out interesting effects of additional massless Dirac fermions with
N_F colors upon the critical behavior of the Ginzburg-Landau model. For
increasing N_F, the model is driven into the type II regime of
superconductivity. The critical exponents are given as a function of N_F.Comment: RevTex4, 4 pages, 1 figure; author information and latest update to
this paper at http://www.physik.fu-berlin.de/~kleinert/institution.html;
version 2: new references and comments on chiral symmetry breaking adde
Magnetic field induced finite size effect in type-II superconductors
We explore the occurrence of a magnetic field induced finite size effect on
the specific heat and correlation lengths of anisotropic type-II
superconductors near the zero field transition temperature Tc. Since near the
zero field transition thermal fluctuations are expected to dominate and with
increasing field strength these fluctuations become one dimensional, whereupon
the effect of fluctuations increases, it appears unavoidable to account for
thermal fluctuations. Invoking the scaling theory of critical phenomena it is
shown that the specific heat data of nearly optimally doped YBa2Cu3O7-x are
inconsistent with the traditional mean-field and lowest Landau level
predictions of a continuous superconductor to normal state transition along an
upper critical field Hc2(T). On the contrary, we observe agreement with a
magnetic field induced finite size effect, whereupon even the correlation
length longitudinal to the applied field H cannot grow beyond the limiting
magnetic length L(H). It arises because with increasing magnetic field the
density of vortex lines becomes greater, but this cannot continue indefinitely.
L(H) is then roughly set on the proximity of vortex lines by the overlapping of
their cores. Thus, the shift and the rounding of the specific heat peak in an
applied field is traced back to a magnetic field induced finite size effect in
the correlation length longitudinal to the applied field.Comment: 8 pages, 4 figure
Critical behaviour of the Ginzburg-Landau model in the type II region
We study the critical behaviour of the three-dimensional U(1) gauge+Higgs
theory (Ginzburg-Landau model) at large scalar self-coupling \lambda (``type II
region'') by measuring various correlation lengths as well as the
Abrikosov-Nielsen-Olesen vortex tension. We identify different scaling regions
as the transition is approached from below, and carry out detailed comparisons
with the criticality of the 3d O(2) symmetric scalar theory.Comment: Lattice2001(higgssusy), 3 page
Self-Duality in Superconductor-Insulator Quantum Phase Transitions
It is argued that close to a Coulomb interacting quantum critical point, the
interaction between two vortices in a disordered superconducting thin film
separated by a distance changes from logarithmic in the mean-field region
to in the region dominated by quantum critical fluctuations. This gives
support to the charge-vortex duality picture of the observed reflection
symmetry in the current-voltage characteristics on both sides of the
transition.Comment: 4 pages, no figures, 2nd version: title (slightly) changed and text
accordingl
Numerical study of duality and universality in a frozen superconductor
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 behavior
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.Comment: 17 pages, 18 figures. Updated to match the version published in PRB
(http://link.aps.org/abstract/PRB/v67/e014525) on 27 Jan 200
Scaling critical behavior of superconductors at zero magnetic field
We consider the scaling behavior in the critical domain of superconductors at
zero external magnetic field. The first part of the paper is concerned with the
Ginzburg-Landau model in the zero magnetic field Meissner phase. We discuss the
scaling behavior of the superfluid density and we give an alternative proof of
Josephson's relation for a charged superfluid. This proof is obtained as a
consequence of an exact renormalization group equation for the photon mass. We
obtain Josephson's relation directly in the form , that
is, we do not need to assume that the hyperscaling relation holds. Next, we
give an interpretation of a recent experiment performed in thin films of
. We argue that the measured mean field like
behavior of the penetration depth exponent is possibly associated with a
non-trivial critical behavior and we predict the exponents and
for the correlation lenght and specific heat, respectively. In the
second part of the paper we discuss the scaling behavior in the continuum dual
Ginzburg-Landau model. After reviewing lattice duality in the Ginzburg-Landau
model, we discuss the continuum dual version by considering a family of
scalings characterized by a parameter introduced such that
, where is the bare mass of the magnetic
induction field. We discuss the difficulties in identifying the renormalized
magnetic induction mass with the photon mass. We show that the only way to have
a critical regime with is having , that
is, with having the scaling behavior of the renormalized photon mass.Comment: RevTex, 15 pages, no figures; the subsection III-C has been removed
due to a mistak
Anomalous dimensions and phase transitions in superconductors
The anomalous scaling in the Ginzburg-Landau model for the superconducting
phase transition is studied. It is argued that the negative sign of the
exponent is a consequence of a special singular behavior in momentum space. The
negative sign of comes from the divergence of the critical correlation
function at finite distances. This behavior implies the existence of a Lifshitz
point in the phase diagram. The anomalous scaling of the vector potential is
also discussed. It is shown that the anomalous dimension of the vector
potential has important consequences for the critical dynamics in
superconductors. The frequency-dependent conductivity is shown to obey the
scaling . The prediction is
obtained from existing Monte Carlo data.Comment: RevTex, 20 pages, no figures; small changes; version accepted in PR