# 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

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

57. 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.

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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. Our ap-proach is as follows: we perform a simple transformation which maps the PT model to a sine-Gordon model with ad-ditional terms depending only on the total topological “charge” of the system and on the driving wave vector Q. 2012-02-16 · The sine-Gordon model is discussed and analyzed within the framework of the renormalization group 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.

1 Klein-Gordon equation is the first relativistic version of the Schrödinger equation for spinless. particles Renormalization is a way. Functional renormalization group approach to correlated fermion systems.

## 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 dimensionless coupling constant.

Note the common crossing at d = 2. - "Structure of the broken phase of the sine-Gordon model using functional renormalization" sine-Gordon model J. Mateos Guilarte The classical action and the ﬁeld equations Solitary waves: kinks, solitons, and breathers The sine- Gordon Hamiltonian: more conserved charges Lectures on Quantum sine-Gordon Models Juan Mateos Guilarte1;2 1Departamento de … 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 sine-Gordon model has a universality and appears in various fields of physics [1-4].

### -function of the sine-Gordon model taking explicitly into account the period-icity. of interaction. the. 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 the ﬁxed points. The results at vanishing frequency. β. 2

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 the ﬁxed points.

57. 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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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. 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 2005-05-31 · Abstract: 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 dimensionless coupling constant.

Re-scaled Action for the sine-Gordon model. Renormalization group flows equations of the sine-Gordon model. Kosterlitz-Thouless Phase Diagram .

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### 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 compactified theory with controllable vortex activity. In the continuum limit the theory has a phase in which the kink current is anomalous, with divergence given by the vortex density.

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 of a perturbation expansion and we derive beta functions of the renormalization group theory.

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### 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.

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 Renormalization Group Theory&Sine-Gordon Model.