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Dynamics of Quarks and Leptons - KTH Physics

R(r1 − r2) = 〈 16 Feb 2012 The sine-Gordon model is discussed and analyzed within the framework of the renormalization group theory. A perturbative renormalization Known Bethe ansatz results about the sine–Gordon factorized scattering are reinterpreted in terms of perturbed conformal field theory. We obtain an exact 25 Feb 2021 The beta functions are calculated for the sine-Gordon model with multiple cosine interactions. The second-order correction in the renormalization Sine-Gordon models. C-function. Results.

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Indeed, let u(x) = ’(x). 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.

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.

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In the continuum limit the theory has a phase in which the kink current is anomalous, with divergence given by the vortex density. important calculation since sine-Gordon-type Hamiltonians are common in the one-dimensional world and we will have to learn how to deal with them in more complicated situations as well. 2.3.2 Renormalization equations for sine-Gordon Hamiltonians To complete our analysis of the spin sector we have to treat the sine-Gordon Hamiltonian (2.106). We present the dimensional regularization approach to the renormalization group theory of the generalized sine-Gordon model.

### 40 YEARS OF BEREZINSKII-KOSTERLITZ-THOULESS THEORY

A perturbative renormalization group procedure is carried out through a decomposition of the sine-Gordon field in slow and fast modes. An effective slow modes's theory is derived and re-scaled to obtain the model's flow equations. Sine-Gordon Model: Renormalization Group Solution and Applications Abstract. The sine-Gordon model is discussed and analyzed within the framework of the renormalization group theory. Introduction. The sine-Gordon model was originally proposed as a toy model for interacting quantum field theories.

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. The vertex interaction is given by cos(k j · φ) where k j (j = 1, 2, …, M) are momentum vectors and φ is an N-component scalar field. OSTI.GOV Journal Article: Comparison of renormalization group schemes for sine-Gordon-type models
The renormalization group is a fundamental and powerful tool to investigate the property of quantum systems [1–15].The physics of a many-body system is sometimes captured by the analysis of an effective field theory model [16–19].Typically, effective field theory models are the ϕ 4 model, the non-linear sigma model and the sine-Gordon model. Each of these models represents universality as
CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We analyse the renormalizability of the sine–Gordon model by the example of the two–point causal Green function up to second order in αr(M 2), the dimensional coupling constant defined at the normalization scale M, and to all orders in β 2, the dimensionless coupling constant. The sine-Gordon equation is a nonlinear hyperbolic partial differential equation in 1 + 1 dimensions involving the d'Alembert operator and the sine of the unknown function.

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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 sine-Gordon model has a universality and appears in various fields of physics [1-4]. The two-dimensional (2D) sine-Gordon model describes the Kosterlitz-Thouless transition of the 2D classical XY model [5,6]. The 2D sine-Gordon model is mapped to the Coulomb gas model … 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. We show that a finite size prediction based on perturbative renormalization group (RG) arguments agrees well with new high precision simulations for small coupling and 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 We shall use a functional renormalization-group RG scheme to study the model at ﬁnite temperatures.

The sine-Gordon model is discussed and analyzed within the framework of the renormalization group theory. A perturbative renormalization group procedure is
1980-10-01 · A momentum space renormalization is presented for the sine-Gordon model with an arbitrary cut-off function. In contrast to previous work the present method reproduces the slope of the critical line as found from the Kosterlitz renormalization of the equivalent Coulomb gas and is also applicable to the case of a sharp cut-off function. We use a renormalization group differential equation to rigorously control the renormalization group flow in a hierarchical lattice Sine-Gordon field theory in the Kosterlitz-Thouless phase. Renormalization group flow of a hierarchical Sine-Gordon model by partial differential equations | SpringerLink
The functional renormalization group treatment is presented for the two-dimensional sine-Gordon model including a bilocal term in the potential, which contributes to the flow at the tree level. It is shown that the flow of the bilocal term can substitute the evolution of the wave function renormalization constant, since it can recover the Kosterlitz–Thouless type phase transition.

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Abstract. The well-known phase structure of the two- dimensional sine-Gordon model is reconstructed by means of its renormalization group 25 Jan 2020 Invariant Gibbs dynamics for the dynamical sine-Gordon model After introducing a suitable renormalization, we first construct the Gibbs 23 Sep 2011 fermions - there is another theory, the massive Thirring model, that Measuring the quantum sine-Gordon kink mass numerically is a challenge, since one and can be renormalized [17] to produce the result for the mass 6 Dec 2017 1+1 dimensional sine-Gordon model perturbatively in the coupling. A CFT describes a fixed point under renormalization group (RG) of a 22 Feb 2017 Decoupling the SU(N)_2-homogeneous Sine-Gordon model The renormalization group flow is studied and we find a precise rule, depending Collective coordinate analysis for adding a space dependent potential to the double sine-Gordon model is presented. Interaction of solitons with a delta function In this paper a nonlocal generalization of the sine-Gordon equation, u(tt)+sin u=( In particular, some solutions of the sine-Gordon model (for example, traveling Example: Tensor-network representation of the Clock Model. = − Tensor network renormalization (TNR, Evenbly, Vidal 2015) Sine-Gordon Model:.

potential. the c. The. along. integration of -function trajectories of the non-perturbative renormalization group ﬂow gives access to the central charges of the model in …
2015-12-01
Dimensional Regularization Approach to the Renormalization Group Theory of the Generalized Sine-Gordon Model TakashiYanagisawa single-cosine potential (conventional sine-Gordon model).

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In contrast to previous work the present method reproduces the slope of the critical line as found from the Kosterlitz renormalization of the equivalent Coulomb gas and is also applicable to the case of a sharp cut-off function. The functional renormalization group treatment is presented for the two-dimensional sine-Gordon model including a bilocal term in the potential, which contributes to the flow at the tree level. It is shown that the flow of the bilocal term can substitute the evolution of the wave function renormalization constant, since it can recover the Kosterlitz–Thouless type phase transition. 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.

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SUMMARY OF THE LECTURES. Lecture 2. January 21st.

## Group Theory and Symmetries in Particle Physics - Chalmers

The same equations are obtained using both these methods. 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.

the. potential.