Symmetries and phase structure of the layered sine-Gordon model

Abstract

Abstract. The phase structure of the layered sine-Gordon (LSG) model is investigated in terms of symmetry considerations by means of differential renormalization group (RG) method using the local potential approximation. The RG analysis of the general N -layer model provides us with the possibility to consider the dependence of the vortex dynamics on the number of layers. The Lagrangians are distinguished according to the number of zero eigenvalues of their mass matrices where the number is found to be decisive with respect to the phase structure of the N -layer models, with neighbouring layers being coupled by terms quadratic in the field variables. It is shown that the LSG model with N layers undergoes a Kosterlitz-Thouless type phase transition at the critical value of the parameter β 2 c = 8N π. In the limit of infinitely many layers the LSG model can be considered as the discretized version of the three-dimensional sine-Gordon model which has been shown to have a single phase within the local potential approximation. The infinite critical value of the parameter β 2 c for the LSG model in the continuum limit (N → ∞) is consistent with the latter observation.

Massless fermions in multiflavorQED2

“…Since in our model β 2 = 4π the spinodal instability always occurs. It was shown [33] that in this phase the couplings u n1n2 are relevant at least in the UV region.…”

“…As in [6,21] we obtained that the higher modes do not affect the scaling of the fundamental mode. However the other couplings flow by different scaling behavior as obtained by an extended UV RG approach [17,33]. We started the evolution with the WH-RG method then at the scale k SI we turned to the tree level blocking equations.…”

Renormalization of QCD2

“…Inserting the ansatz (3.5) into eq. (3.4), the right-hand side becomes periodic, while the left-hand side contains both periodic and non-periodic parts [14,[49][50][51][52]. The non-periodic part contains only mass terms, so that we obtain a RG flow equation for the dimensionless mass matrix 6) giving the scalingJ…”

“…The correct UV scaling can be obtained if we improve the results of the linearized approximation by taking into account corrections of the order O(J) for the QCD 2 type and those of O(G) for the QED 2 type case [14,24,25,[49][50][51]. This is achieved by linearizing the RG equation in the periodic piece of the blocked potential,…”

“…Therefore, for sufficiently small bare couplingỹ(Λ), there exists only a single phase [14,24,25,[49][50][51] in the N = 1 layer model, i.e., the couplingỹ(k) is relevant (increasing) in the IR limit (k → 0) irrespectively of β 2 . For N → ∞ the magnetically coupled LSG behaves like a massless 2D-SG model with the critical frequency β 2 c = 8π [13].…”