Related papers: Functional renormalization group approach to the s…
We investigate the previously proposed cyclic regime of the Kosterlitz-Thouless renormalization group (RG) flows. The period of one cycle is computed in terms of the RG invariant. Using bosonization, we show that the theory has $U_q…
We investigate the renormalization group theory of generalized multi-vertex sine-Gordon model by employing the dimensional regularization method and also the Wilson renormalization group method. The vertex interaction is given by…
A renormalization group theory for a system consisting of coupled superconducting layers as a model for typical high-temperature superconducters is developed. In a first step the electromagnetic interaction over infinitely many layers is…
We show that four-dimensional systems may exhibit a topological phase transition analogous to the well-known Berezinskii-Kosterlitz-Thouless vortex unbinding transition in two-dimensional systems. The realisation of an engineered quantum…
The idea of the functional renormalization group and one-loop improved renormalization group flows are reviewed. The associated flow equations and nonperturbative approximations schemes for its solutions are discussed. These techniques are…
Using the renormalisation group (RG) we study two dimensional electromagnetic coulomb gas and extended Sine-Gordon theories invariant under the modular group SL(2,Z). The flow diagram is established from the scaling equations, and we derive…
The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for…
The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type Universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the…
These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general…
One-dimensional systems of interacting atoms are an ideal laboratory to study the Kosterlitz-Thouless phase transition. In the renormalization group picture there is essentially a two-parameter phase diagram to explore. We first present how…
Working with scalar field theories, we discuss choices of regulator that, inserted in the functional renormalization group equation, reproduce the results of dimensional regularization at one and two loops. The resulting flow equations can…
Numerous correlated electron systems exhibit a strongly scale-dependent behavior. Upon lowering the energy scale, collective phenomena, bound states, and new effective degrees of freedom emerge. Typical examples include (i) competing…
We derive a new renormalization group to calculate a non-trivial critical exponent of the divergent correlation length which gives a universality classification of essential singularities in infinite-order phase transitions. This method…
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…
The phase structure of a higher derivative sine-Gordon model in four dimensions is analysed. It is shown that the inclusion of a relevant two-derivative term in the action significantly modifies some of the results obtained by neglecting…
A field theoretic renormalization group method is presented which is capable of dealing with crossover problems associated with a change in the upper critical dimension. The method leads to flow functions for the parameters and coupling…
We analyse the renormalizability of the sine-Gordon model by the example of the two-point Green function up to second order in alpha_r(M), the dimensional coupling constant defined at the normalization scale M, and to all orders in beta^2,…
The functional renormalization group (fRG) approach has the property that, in general, the flow equation for the two-particle vertex generates $\mathcal{O}(N^4)$ independent variables, where $N$ is the number of interacting states (e.g.…
We review a formulation of a renormalization-group scheme for Hamiltonian systems with two degrees of freedom. We discuss the renormalization flow on the basis of the continued fraction expansion of the frequency. The goal of this approach…
We present a renormalization group analysis for the hyperbolic sine-Gordon (sinh-Gordon) model in two dimensions. We derive the renormalization group equations based on the dimensional regularization method and the Wilson method. The same…