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

Renormalization group in internal space

Renormalization group in the internal space consists of the gradual change of the coupling constants. Functional evolution equations corresponding to the change of the mass or the coupling constant are presented in the framework of a scalar model. The evolution in the mass which yields the functional generalization of the Callan-Symanzik equation for the one-particle irreducible effective action is given in its renormalized, cutoff-independent form. The evolution of the coupling constant generates an evolution equation for the two-particle irreducible effective action. © 2005 The American Physical Society

Quantum censorship in two dimensions

It is pointed out that increasingly attractive interactions, represented by partially concave local potential in the Lagrangian, may lead to the degeneracy of the blocked, renormalized action at the gliding cutoff scale by tree-level renormalization. A quantum counterpart of this mechanism is presented in the two-dimensional sine-Gordon model. The presence of Quantum Censorship is conjectured which makes the loop contributions pile up during the renormalization and thereby realize an approximate semiclassical effect.Comment: 12 pages, 4 figures. Final versio

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

Onset of symmetry breaking by the functional RG method

A numerical algorithm is used to solve the bare and the effective potential for the scalar $\phi^4$ model in the local potential approximation. An approximate dynamical Maxwell-cut is found which reveals itself in the degeneracy of the action for modes at some scale. This result indicates that the potential develop singular field dependence as far as one can see it by an lgorithm of limited numerical accuracyComment: 19 pages, 10 figures, accepted version. To appear in International Journal of Modern Physics

Generalized universality in the massive sine-Gordon model

A non-trivial interplay of the UV and IR scaling laws, a generalization of the universality is demonstrated in the framework of the massive sine-Gordon model, as a result of a detailed study of the global behaviour of the renormalization group flow and the phase structure.Comment: 9 pages, 7 figure

Interplay of fixed points in scalar models

We performed the renormalization group analysis of scalar models exhibiting spontaneous symmetry breaking. It is shown that an infrared fixed point appears in the broken symmetric phase of the models, which induces a dynamical scale, that can be identified with the correlation length. This enables one to identify the type of the phase transition which shows similarity to the one appearing in the crossover scale. The critical exponent $\nu$ of the correlation length also proved to be equal in the crossover and the infrared scaling regimes.Comment: 11 pages, 4 figure

Functional Callan-Symanzik equation for QED

An exact evolution equation, the functional generalization of the Callan-Symanzik method, is given for the effective action of QED where the electron mass is used to turn the quantum fluctuations on gradually. The usual renormalization group equations are recovered in the leading order but no Landau pole appears.Comment: 9 pages, no figure

Functional renormalization group approach to the sine-Gordon model

The renormalization group flow is presented for the two-dimensional sine-Gordon model within the framework of the functional renormalization group method by including the wave-function renormalization constant. The Kosterlitz-Thouless-Berezinski type phase structure is recovered as the interpolating scaling law between two competing IR attractive area of the global renormalization group flow.Comment: 4 pages, 3 figure