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

Renormalization-Group Analysis of Layered Sine-Gordon Type Models

We analyze the phase structure and the renormalization group (RG) flow of the generalized sine-Gordon models with nonvanishing mass terms, using the Wegner-Houghton RG method in the local potential approximation. Particular emphasis is laid upon the layered sine-Gordon (LSG) model, which is the bosonized version of the multi-flavour Schwinger model and approaches the sum of two ``normal'', massless sine-Gordon (SG) models in the limit of a vanishing interlayer coupling J. Another model of interest is the massive sine-Gordon (MSG) model. The leading-order approximation to the UV (ultra-violet) RG flow predicts two phases for the LSG as well as for the MSG, just as it would be expected for the SG model, where the two phases are known to be separated by the Coleman fixed point. The presence of finite mass terms (for the LSG and the MSG) leads to corrections to the UV RG flow, which are naturally identified as the ``mass corrections''. The leading-order mass corrections are shown to have the following consequences: (i) for the MSG model, only one phase persists, and (ii) for the LSG model, the transition temperature is modified. Within the mass-corrected UV scaling laws, the limit of J -> 0 is thus nonuniform with respect to the phase structure of the model. The modified phase structure of general massive sine-Gordon models is connected with the breaking of symmetries in the internal space spanned by the field variables. For the LSG, the second-order subleading mass corrections suggest that there exists a cross-over regime before the IR scaling sets in, and the nonlinear terms show explicitly that higher-order Fourier modes appear in the periodic blocked potential.Comment: 27 pages, 7 figure

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

Wave-function renormalization for the Coulomb-gas in Wegner-Houghton's RG method

The RG flow for the sine-Gordon model is determined by means of the method of Wegner and Houghton in next-to-leading order of the derivative expansion. For small values of the fugacity this agrees with the well-known RG flow of the two-dimensional Coulomb-gas found in the dilute gas approximation and a systematic way of obtaining higher-order corrections to this approximation is given.Comment: 4 pages, 2 figure

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 $1+1$ 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.