# Renormalization Group Theory&Sine-Gordon Model. SUMMARY OF THE LECTURES. Lecture 2. January 21st. Renormalization Group Theory . General procedure III: Averaging in the fast modes’ ground state. Sine-Gordon Model. Conceptual overview. The model. Re-scaled Action for the sine-Gordon model. Renormalization group flows equations of the sine-Gordon model.

The sine-Gordon model is discussed and analyzed within the framework of the renormalization group theory. A perturbative renormalization group procedure is described, in which the sine-Gordon field

January 23rd. Sine-Gordon Model. Re-scaled Action for the sine-Gordon model. Renormalization group flows equations of the sine-Gordon model.

Then the action Functional Renormalization Group Approach to the Sine-Gordon Model S. Nagy,1 I. Na´ndori,2 J. Polonyi,3 and K. Sailer1 1Department of Theoretical Physics, University of Debrecen, Debrecen, Hungary 2Institute of Nuclear Research, P.O. Box 51, H-4001 Debrecen, Hungary 3Strasbourg University, CNRS-IPHC, BP28 67037 Strasbourg Cedex 2, France The chiral sine-Gordon model is a model for G-valued fields and describes a new class of phase transitions, where G is a compact Lie group. We show that the model is renormalizable by means of a perturbation expansion and we derive beta functions of the renormalization group theory. arXiv:hep-th/0509100v1 14 Sep 2005 Renormalization–Group Analysis of Layered Sine–Gordon Type Models I. Nandori´ 1,2, S. Nagy3, K. Sailer3 and U. D. Jentschura2 1Institute of Nuclear Research of the Hungarian Academy of Sciences, Sine-Gordon Model and Renormalization Group Predictions David J. Lancaster Department of Computer Science Westminster University Juan J. Ruiz-Lorenzo Departamento de F¶‡sica Universidad de Extremadura Instituto de Biocomputaci¶on y F¶‡sica de los Sistemas Complejos [BIFI](UZ) D.J.Lancaster@westminster.ac.uk, ruiz@unex.es Renormalization of the Sine-Gordon model To learn more about the phase transition, we need to perform an explicit RG calculation. The good news about the SG model is that we can do so using the standard Wilson RG momentum shell approach. Since this approach is already familiar, we only outline the main steps. 1) We treat the Gaussian part of Title: Numerical simulations of the random phase sine-Gordon model and renormalization group predictions: Authors: Lancaster, D.J. and Ruiz-Lorenzo, J.J. Abstract: Numerical simulations of the random phase sine-Gordon model suffer from strong finite size effects preventing the non-Gaussian log2 r component of the spatial correlator from following the universal infinite volume prediction. Ultraviolet renormalization was done in the frame of the Bethe Ansatz.

## Abstract. 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-theoretic models discussing the applicability of various functional RG methods in detail.

They are the non- linear sigma model, the φ4 model and the sine-Gordon model. We use the dimensional regularization method to regularize the divergence and It appears that the sinh-Gordon model is similar to the ϕ4 model when we expand coshϕ in terms of ϕ. In fact, both models The beta functions are calculated for the sine-Gordon model with multiple cosine interactions. The second- the layered XY model which can be mapped onto the layered sine-Gordon model.

### 2005-05-31

Sine-Gordon Model. Re-scaled Action for the sine-Gordon model. Renormalization group flows equations of the sine-Gordon model.

The vortex-dominated properties of high transition temperature superconductors with extremely
-function of the sine-Gordon model taking explicitly into account the period-icity. of interaction. the. potential. the c.

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WKB formula for the mass of quantum breather. therein for the results on the sine-Gordon massless model using the quantum inverse scattering method).

We use the dimensional regularization method to regularize the divergence and
It appears that the sinh-Gordon model is similar to the ϕ4 model when we expand coshϕ in terms of ϕ.

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### Chiral Sine-Gordon(˜SG) model can be mapped into or-dinary Sine-Gordon(SG) theory, but we now know that this is wrong. The RG behavior of ˜SG theory is com-pletely di erent(and somewhat much more simpler) than SG theory, and it shows that relevance of tunneling be-tween double-layer edge modes changes according to bulk topological structure.

The phase structure is quite complicated. We investigate the chiral sine-Gordon model using the renormalization group method. The chiral sine-Gordon model is a model for G-valued ﬁelds and describes a new class of phase transitions, where G is a compact Lie group. 1991-02-01 OSTI.GOV Journal Article: Renormalization of the Sine-Gordon model and nonconservation of the kink current Abstract – We investigate the chiral sine-Gordon model using the renormalization group method. The chiral sine-Gordon model is a model for G-valued ﬁelds and describes a new class of phase transitions, where G is a compact Lie group. We show that the model is renormalizable by means We renormalize the (1+1)-dimensional sine-Gordon model by placing it on a Euclidean lattice, and study the renormalization group flow. We start with a compac 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.