Asymptotic low-temperature behavior of two-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>RP</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>models

Bonati, Claudio; Franchi, Alessio; Pelissetto, Andrea; Vicari, Ettore

doi:10.1103/physrevd.102.034513

Cited by 19 publications

(28 citation statements)

References 58 publications

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“…We show that the FSS curves (18) of the Binder parameter U versus R ξ computed in the model (2) agree with those computed in RP N−1 models (we use the results reported in Ref. [23]). These results provide numerical evidence that, for N c ≥ 3, the critical behavior belongs to the universality class of the 2D RP N f −1 field theory, in agreement with the arguments of the previous section.…”

Section: Numerical Resultssupporting

confidence: 74%

“…In the same figure, we also report data for the standard RP 2 lattice model with action (9), and for the RP 2 gauge model with action (10) (as shown in Ref. [23], the data for L ¼ 320 provide a good approximation of the asymptotic curve). The RP 2 results are consistent with the asymptotic FSS curve for the SOðN c Þ gauge model, confirming our claim…”

Section: Numerical Resultsmentioning

confidence: 74%

“…The horizontal dashed line indicates the R ξ → 0 limit U ¼ 11=9. Data approach the same universal FSS curve obtained for the RP 3 models, for which we show MC data for the model (10) taken from Ref [23]…”

mentioning

confidence: 84%

“…The nature of their low-temperature behavior for N ≥ 3 has been the object of a long debate-see, e.g., Refs. [19][20][21][22][23].…”

Section: The Multiflavor Lattice So(n C ) Gauge Modelmentioning

confidence: 99%

“…We refer to Ref. [23] for a thorough discussion of this point. There, we report extensive numerical results that indicate that the universal low-temperature long-distance behavior of the 2D RP N−1 models differs from that of the 2D OðNÞ vector models: they appear as distinct universality classes.…”

Section: The Multiflavor Lattice So(n C ) Gauge Modelmentioning

confidence: 99%

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Asymptotic low-temperature critical behavior of two-dimensional multiflavor lattice SO(Nc) gauge theories

et al. 2020

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We address the interplay between global and local gauge non-Abelian symmetries in lattice gauge theories with multicomponent scalar fields. We consider two-dimensional lattice scalar non-Abelian gauge theories with a local SOðN c Þ (N c ≥ 3) and a global OðN f Þ invariance, obtained by partially gauging a maximally OðN f N c Þ-symmetric multicomponent scalar model. Correspondingly, the scalar fields belong to the coset S N f N c −1 =SOðN c Þ, where S N is the N-dimensional sphere. In agreement with the Mermin-Wagner theorem, these lattice SOðN c Þ gauge models with N f ≥ 3 do not have finite-temperature transitions related to the breaking of the global non-Abelian OðN f Þ symmetry. However, in the zero-temperature limit they show a critical behavior characterized by a correlation length that increases exponentially with the inverse temperature, similarly to nonlinear OðNÞ σ models. Their universal features are investigated by numerical finite-size scaling methods. The results show that the asymptotic low-temperature behavior belongs to the universality class of the two-dimensional RP N f −1 model.

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Section: Numerical Resultssupporting

confidence: 74%

Section: Numerical Resultsmentioning

confidence: 74%

mentioning

confidence: 84%

“…The nature of their low-temperature behavior for N ≥ 3 has been the object of a long debate-see, e.g., Refs. [19][20][21][22][23].…”

Section: The Multiflavor Lattice So(n C ) Gauge Modelmentioning

confidence: 99%

Section: The Multiflavor Lattice So(n C ) Gauge Modelmentioning

confidence: 99%

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Asymptotic low-temperature critical behavior of two-dimensional multiflavor lattice SO(Nc) gauge theories

et al. 2020

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Two-dimensional lattice SU(Nc) gauge theories with multiflavor adjoint scalar fields

Bonati

Franchi

Pelissetto

et al. 2021

J. High Energ. Phys.

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We consider two-dimensional lattice SU(Nc) gauge theories with Nf real scalar fields transforming in the adjoint representation of the gauge group and with a global O(Nf) invariance. Focusing on systems with Nf≥ 3, we study their zero-temperature limit, to understand under which conditions a continuum limit exists, and to investigate the nature of the associated quantum field theory. Extending previous analyses, we address the role that the gauge-group representation and the quartic scalar potential play in determining the nature of the continuum limit (when it exists). Our results further corroborate the conjecture that the continuum limit of two-dimensional lattice gauge models with multiflavor scalar fields, when it exists, is associated with a σ model defined on a symmetric space that has the same global symmetry as the lattice model.

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Critical points in the CP ^N−1 model

Diouane¹,

Lamsen²,

Delfino³

2022

J. Stat. Mech.

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We use scale invariant scattering theory to obtain the exact equations determining the renormalization group fixed points of the two-dimensional CP N−1 model, for N real. Also due to special degeneracies at N = 2 and 3, the space of solutions for N ⩾ 2 reduces to that of the O(N 2 − 1) model, and accounts for a zero temperature critical point. For N < 2 the space of solutions becomes larger than that of the O(N 2 − 1) model, with the appearance of new branches of fixed points relevant for criticality in gases of intersecting loops.

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Asymptotic low-temperature behavior of two-dimensionalRPN−1models

Cited by 19 publications

References 58 publications

Asymptotic low-temperature critical behavior of two-dimensional multiflavor lattice SO(Nc) gauge theories

Asymptotic low-temperature critical behavior of two-dimensional multiflavor lattice SO(Nc) gauge theories

Two-dimensional lattice SU(Nc) gauge theories with multiflavor adjoint scalar fields

Critical points in the CP ^N−1 model

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Asymptotic low-temperature behavior of two-dimensionalRPN−1models

Cited by 19 publications

References 58 publications

Asymptotic low-temperature critical behavior of two-dimensional multiflavor lattice SO(Nc) gauge theories

Asymptotic low-temperature critical behavior of two-dimensional multiflavor lattice SO(Nc) gauge theories

Two-dimensional lattice SU(Nc) gauge theories with multiflavor adjoint scalar fields

Critical points in the CP N−1 model

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Product

Resources

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Critical points in the CP ^N−1 model