34 research outputs found
Length-scale-dependent phase transition in BSCCO single crystals
Electrical transport measurements using a multiterminal configuration are
presented, which prove that in BSCCO single crystals near the transition
temperature in zero external magnetic field the secondary voltage is induced by
thermally activated vortex loop unbinding. The phase transition between the
bound and unbound states of the vortex loops was found to be below the
temperature where the phase coherence of the superconducting order parameter
extends over the whole volume of the sample. We show experimentally that 3D/2D
phase transition in vortex dimensionality is a length-scale-dependent layer
decoupling process and takes place simultaneously with the 3D/2D phase
transition in superconductivity at the same temperature.Comment: 14 pages, 4 figures, to be published in Philos. Ma
Effective Action and Phase Structure of Multi-Layer Sine-Gordon Type Models
We analyze the effective action and the phase structure of N-layer
sine-Gordon type models, generalizing the results obtained for the two-layer
sine-Gordon model found in [I. Nandori, S. Nagy, K. Sailer and U. D.
Jentschura, Nucl. Phys. B725, 467-492 (2005)]. Besides the obvious field
theoretical interest, the layered sine-Gordon model has been used to describe
the vortex properties of high transition temperature superconductors, and the
extension of the previous analysis to a general N-layer model is necessary for
a description of the critical behaviour of vortices in realistic multi-layer
systems. The distinction of the Lagrangians in terms of mass eigenvalues is
found to be the decisive parameter with respect to the phase structure of the
N-layer models, with neighbouring layers being coupled by quadratic terms in
the field variables. By a suitable rotation of the field variables, we identify
the periodic modes (without explicit mass terms) in the N-layer structure,
calculate the effective action and determine their Kosterlitz-Thouless type
phase transitions to occur at a coupling parameter \beta^2_{c} = 8 N \pi, where
N is the number of layers (or flavours in terms of the multi-flavour Schwinger
model).Comment: 15 page
Differential Renormalization-Group Approach to the Layered sine-Gordon Model
New qualitative picture of vortex length-scale dependence has been found in
recent electrical transport measurements performed on strongly anisotropic
BSCCO single crystals in zero magnetic field. This indicates the need for a
better description of the 3D/2D crossover in vortex dimensionality. The
vortex-dominated properties of high transition temperature superconductors with
extremely high anisotropy (layered systems) are reasonably well described in
the framework of the layered XY model which can be mapped onto the layered
sine-Gordon model. For the latter we derive an exact renormalization group (RG)
equation using Wegner's and Houghton's approach in the local potential
approximation. The agreement of the UV scaling laws find by us by linearizing
the RG equations with those obtained previously in the literature in the dilute
gas approximation makes the improvement appearant which can be achieved by
solving our RG equations numerically.Comment: 12 pages, no figures, to be published in Philos. Ma
Berezinskii-Kosterlitz-Thouless transition and criticality of an elliptic deformation of the sine-Gordon model
We introduce and study the properties of a periodic model interpolating
between the sine-- and the sinh--Gordon theories in dimensions. This
model shows the peculiarities, due to the preservation of the functional form
of their potential across RG flows, of the two limiting cases: the sine-Gordon,
not having conventional order/magnetization at finite temperature, but
exhibiting Berezinskii-Kosterlitz-Thouless (BKT) transition; and the
sinh-Gordon, not having a phase transition, but being integrable. The
considered interpolation, which we term as {\em sn-Gordon} model, is performed
with potentials written in terms of Jacobi functions. The critical properties
of the sn-Gordon theory are discussed by a renormalization-group approach. The
critical points, except the sinh-Gordon one, are found to be of BKT type.
Explicit expressions for the critical coupling as a function of the elliptic
modulus are given.Comment: v2, 10 pages, 8 figures, accepted in J. Phys.
On the renormalization of the bosonized multi-flavor Schwinger model
The phase structure of the bosonized multi-flavor Schwinger model is
investigated by means of the differential renormalization group (RG) method. In
the limit of small fermion mass the linearized RG flow is sufficient to
determine the low-energy behavior of the N-flavor model, if it has been rotated
by a suitable rotation in the internal space. For large fermion mass, the exact
RG flow has been solved numerically. The low-energy behavior of the
multi-flavor model is rather different depending on whether N=1 or N>1, where N
is the number of flavors. For N>1 the reflection symmetry always suffers
breakdown in both the weak and strong coupling regimes, in contrary to the N=1
case, where it remains unbroken in the strong coupling phase.Comment: 13 pages, 2 figures, final version, published in Physics Letters
Applicability of layered sine-Gordon models to layered superconductors: II. The case of magnetic coupling
In this paper, we propose a quantum field theoretical renormalization group
approach to the vortex dynamics of magnetically coupled layered
superconductors, to supplement our earlier investigations on the
Josephson-coupled case. We construct a two-dimensional multi-layer sine-Gordon
type model which we map onto a gas of topological excitations. With a special
choice of the mass matrix for our field theoretical model, vortex dominated
properties of magnetically coupled layered superconductors can be described.
The well known interaction potentials of fractional flux vortices are
consistently obtained from our field-theoretical analysis, and the physical
parameters (vortex fugacity and temperature parameter) are also identified. We
analyse the phase structure of the multi-layer sine--Gordon model by a
differential renormalization group method for the magnetically coupled case
from first principles. The dependence of the transition temperature on the
number of layers is found to be in agreement with known results based on other
methods.Comment: 7 pages, 1 figure, published in J. Phys.: Condens. Matte
Comparison of renormalization group schemes for sine-Gordon type models
The scheme-dependence of the renormalization group (RG) flow has been
investigated in the local potential approximation for two-dimensional periodic,
sine-Gordon type field-theoric models discussing the applicability of various
functional RG methods in detail. It was shown that scheme-independent
determination of such physical parameters is possible as the critical frequency
(temperature) at which Kosterlitz-Thouless-Berezinskii type phase transition
takes place in the sine-Gordon and the layered sine-Gordon models, and the
critical ratio characterizing the Ising type phase transition of the massive
sine-Gordon model. For the latter case the Maxwell construction represents a
strong constraint on the RG flow which results in a scheme-independent infrared
value for the critical ratio. For the massive sine-Gordon model also the
shrinking of the domain of the phase with spontaneously broken periodicity is
shown to take place due to the quantum fluctuations.Comment: 17 pages, 8 figures, revised version, to be published in Phys. Rev.
c-function and central charge of the sine-Gordon model from the non-perturbative renormalization group flow
In this paper we study the c-function of the sine-Gordon model taking explicitly into account the periodicity of the interaction potential. The integration of the c-function along trajectories of the non-perturbative renormalization group flow gives access to the central charges of the model in the fixed points. The results at vanishing frequency \u3b22, where the periodicity does not play a role, are retrieved and the independence on the cutoff regulator for small frequencies is discussed. Our findings show that the central charge obtained integrating the trajectories starting from the repulsive low-frequencies fixed points (\u3b22<8\u3c0) to the infra-red limit is in good quantitative agreement with the expected \u3b4c=1 result. The behavior of the c-function in the other parts of the flow diagram is also discussed. Finally, we point out that including also higher harmonics in the renormalization group treatment at the level of local potential approximation is not sufficient to give reasonable results, even if the periodicity is taken into account. Rather, incorporating the wave-function renormalization (i.e. going beyond local potential approximation) is crucial to get sensible results even when a single frequency is used
Functional renormalization group with a compactly supported smooth regulator function
The functional renormalization group equation with a compactly supported
smooth (CSS) regulator function is considered. It is demonstrated that in an
appropriate limit the CSS regulator recovers the optimized one and it has
derivatives of all orders. The more generalized form of the CSS regulator is
shown to reduce to all major type of regulator functions (exponential,
power-law) in appropriate limits. The CSS regulator function is tested by
studying the critical behavior of the bosonized two-dimensional quantum
electrodynamics in the local potential approximation and the sine-Gordon scalar
theory for d<2 dimensions beyond the local potential approximation. It is shown
that a similar smoothing problem in nuclear physics has already been solved by
introducing the so called Salamon-Vertse potential which can be related to the
CSS regulator.Comment: JHEP style, 11 pages, 2 figures, proofs corrected, accepted for
publication by JHE