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Nonlinear Dynamics and Renormalization Group - Sigal - Häftad

Renormalization Group Theory . General procedure III: Averaging in the fast modes’ ground state. Sine-Gordon Model. Conceptual overview.

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Kosterlitz-Thouless Phase Diagram . Gap. Red-marked items: updates on the original lecture plan. 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.

The particle spectrum consists of a soliton, an anti-soliton and a finite (possibly zero) number of breathers. The number of the breathers depends on the value of the parameter. Multi particle productions cancels on mass shell.

## 40 YEARS OF BEREZINSKII-KOSTERLITZ-THOULESS THEORY

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.

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Renormalization group flows equations of the sine-Gordon model. 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. Download Citation | Renormalization group theory of generalized multi-vertex sine-Gordon model | We investigate the renormalization group theory of generalized multi-vertex sine-Gordon model by 2018-01-01 dimensional sine-Gordon (SG) model has a well-known phase structure and renormalization group ﬂow but does not easily ﬁt into the general scheme. Our aim in this work is the clariﬁca-tion of these issues by a careful renormalization group study of the SG model. The SG model, deﬁned by the action S = (1) x 1 2 (∂μφx) 2 +u1 cos(βφ), Renormalization Group Theory&Sine-Gordon Model.

Conceptual overview. The model. Re-scaled Action for the sine-Gordon model. Renormalization group flows equations of the sine-Gordon model. 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.

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Conceptual overview.

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.

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