Renormalization of periodic potentials

Nándori, I.; Polónyi, János; Sailer, K.

doi:10.1103/physrevd.63.045022

Cited by 51 publications

(120 citation statements)

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“…This gives a clear explanation in the FRG framework of the presence or the lack of SSB in O(N ) models in d = 2. Of course, the fact that there is no SSB for N = 2 does not imply the absence of the Berezinskii Kosterlitz-Thouless transition [59,60], as can be seen also in FRG treatments [10,[61][62][63].…”

Section: =mentioning

confidence: 99%

Truncation effects in the functional renormalization group study of spontaneous symmetry breaking

Defenu

Mati

Márián

et al. 2015

J. High Energ. Phys.

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Abstract:We study the occurrence of spontaneous symmetry breaking (SSB) for O(N ) models using functional renormalization group techniques. We show that even the local potential approximation (LPA) when treated exactly is sufficient to give qualitatively correct results for systems with continuous symmetry, in agreement with the Mermin-Wagner theorem and its extension to systems with fractional dimensions. For general N (including the Ising model N = 1) we study the solutions of the LPA equations for various truncations around the zero field using a finite number of terms (and different regulators), showing that SSB always occurs even where it should not. The SSB is signalled by Wilson-Fisher fixed points which for any truncation are shown to stay on the line defined by vanishing mass beta functions.

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Section: =mentioning

confidence: 99%

Truncation effects in the functional renormalization group study of spontaneous symmetry breaking

Defenu

Mati

Márián

et al. 2015

J. High Energ. Phys.

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“…The renormalization of a two-dimensional one-component scalar field theory with a periodic self-interaction, and the two-dimensional generalized sine-Gordon model (GSGM) have been investigated for d = 2 dimensions in great detail over the last three decades [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. Here, we only mention some of the main results:…”

Section: Introductionmentioning

confidence: 99%

“…• The blocked potential for the two-dimensional GSGM tends to a constant effective potential in the IR limit, independent of the field [12,13,14].…”

Section: Introductionmentioning

confidence: 99%

Renormalization-group analysis of the generalized sine-Gordon model and of the Coulomb gas for d>~3 dimensions

2004

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Renormalization-group (RG) flow equations have been derived for the generalized sine-Gordon model (GSGM) and the Coulomb gas (CG) in d ≥ 3 of dimensions by means of Wegner's and Houghton's, and by way of the real-space RG approaches. The UV scaling laws determined by the leading-order terms of the flow equations are in qualitative agreement for all dimensions d ≥ 3, independent of the dimensionality, and in sharp contrast to the special case d = 2. For the 4-dimensional GSGM it is demonstrated explicitly (by numerical calculations), that the blocked potential tends to a constant effective potential in the infrared (IR) limit, satisfying the requirements of periodicity and convexity. The comparison of the RG flows for the three-dimensional GSGM, the CG, and the vortex-loop gas reveals a significant dependence on the renormalization schemes and the approximations used.PACS numbers: 11.10.Hi, 11.10.Kk I. INTRODUCTIONThe renormalization of a two-dimensional one-component scalar field theory with a periodic self-interaction, and the two-dimensional generalized sine-Gordon model (GSGM) have been investigated for d = 2 dimensions in great detail over the last three decades [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. Here, we only mention some of the main results:• The blocked potential for the two-dimensional GSGM tends to a constant effective potential in the IR limit, independent of the field [12,13,14].• Following the procedure proposed in [16], one can identically rewrite the partition function of the d-dimensional GSGM in the form of a d-dimensional static Coulomb gas, which we call here the equivalent Coulomb gas (ECG). For d = 2 it is well-known that the GSGM and the ECG, as well as the XY model describing classical planar spins belong to the same universality class [10]. The XY model has a dual theory in the sense of [17] that can be reformulated as a gas of topological excitations: the two-dimensional vortex gas (VG) for d = 2, and the three-dimensional vortex-loop gas (VLG) for d = 3 (see [10] and Refs. therein). For dimensions d = 2, it was shown that the ECG and the VG can be transformed into one another by an appropriate duality transformation [3,7,8,15] that inverts the temperature. Two-dimensional generalized models are well known where both the ECG and the VG are included as particular limiting cases [3,7,8,15] and are self-dual under the duality transformation.While the relations of the various models for two dimensions are well-established, those of the corresponding models for d = 3 are not completely settled (see e.g. [10]). In particular, it is not proven that the VLG and the threedimensional XY-model belong to the same class of universality. Therefore, the investigation of the renormalization of the GSGM and the ECG for d ≥ 3 dimensions is essential for a further clarification of this issue. The purpose of the present work is threefold:1. to investigate the renormalization of the GSGM for dimensions d ≥ 2 by the Wegner-Houghton renormalizationgroup (WH-RG) method [18] and to demonstrate numerically tha...

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“…As we have shown previously in section 3.1 , the multi-color QCD 2 gives values of the parameter β 2 = 4π < β 2 c (N ) for arbitrary number N > 1 of colors, which means that the corresponding SG model is in the symmetry broken phase. Earlier calculations based on Fourier expansion [31,46,[56][57][58] showed that in the symmetry broken phase the effective potential is superuniversal with the parabolic shape (3.8). It happened numerically that the Fourier-expansion drove the evolution towards the pole at a non-vanishing scale.…”

Section: Jhep01(2011)126mentioning

confidence: 99%

“…The functional RG method showed [31,32,56,57] that this SG model has two phases depending on the value of its parameter β 2 /3. As we have shown previously in section 3.1 , the multi-color QCD 2 gives values of the parameter β 2 = 4π < β 2 c (N ) for arbitrary number N > 1 of colors, which means that the corresponding SG model is in the symmetry broken phase.…”

Section: Jhep01(2011)126mentioning

confidence: 99%

Renormalization of QCD2

Kovács

Nagy

Nándori

et al. 2011

J. High Energ. Phys.

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Renormalization of periodic potentials

Cited by 51 publications

References 31 publications

Truncation effects in the functional renormalization group study of spontaneous symmetry breaking

Truncation effects in the functional renormalization group study of spontaneous symmetry breaking

Renormalization-group analysis of the generalized sine-Gordon model and of the Coulomb gas for d>~3 dimensions

Renormalization of QCD2

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Renormalization of periodic potentials

Cited by 51 publications

References 31 publications

Truncation effects in the functional renormalization group study of spontaneous symmetry breaking

Truncation effects in the functional renormalization group study of spontaneous symmetry breaking

Renormalization-group analysis of the generalized sine-Gordon model and of the Coulomb gas for d&gt;~3 dimensions

Renormalization of QCD2

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Renormalization-group analysis of the generalized sine-Gordon model and of the Coulomb gas for d>~3 dimensions