Non-trivial θ-vacuum effects in the 2-d O(3) model

Bögli, Michael; Niedermayer, Ferenc; Pepe, Michele; Wiese, U.‐J.

doi:10.1007/jhep04(2012)117

Cited by 25 publications

(38 citation statements)

References 48 publications

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“…Assuming that the logarithmic violations are known, it is however easy to modify the method in order to overcome this problem. We have then been able to show that our numerical results for sufficiently large β, i.e., for sufficiently weak coupling, are compatible with the expected WZNW-like behaviour at θ = π, in agreement with previous numerical investigations [2,16,17].…”

Section: Discussionsupporting

confidence: 89%

“…Using finite size scaling theory, the authors of Ref. [2,16,17] found a second order phase transition at θ = π, in agreement with Haldane's conjecture, and a finite size scaling in good agreement with the assumption of a WZNW-type of critical behaviour.…”

Section: Introductionsupporting

confidence: 63%

“…Our aim is to understand the origin of the discrepancy between the results of Refs. [2,16,17] and those of Ref. [23].…”

Section: Introductionmentioning

confidence: 83%

“…A first strategy [2,16,17] is based on the determination of the probability distribution of the topological charge by means of simulations at θ = 0, which allows in principle to reconstruct the expectation values of the various observables at θ = 0. In order to achieve the very high accuracy required by this approach, the authors of Refs.…”

Section: Introductionmentioning

confidence: 99%

“…In order to achieve the very high accuracy required by this approach, the authors of Refs. [2,16,17] have employed a constrained ("topological" [18]) action on a triangular lattice, which allows simulations by means of an efficient Wolff cluster algorithm [19]. The parameters of the action were chosen in order to be in the weak-coupling regime.…”

Section: Introductionmentioning

confidence: 99%

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Critical behavior of theO(3)nonlinear sigma model with topological term atθ=πfrom numerical simulations

et al. 2012

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We investigate the critical behaviour at θ = π of the two-dimensional O(3) nonlinear sigma model with topological term on the lattice. Our method is based on numerical simulations at imaginary values of θ, and on scaling transformations that allow a controlled analytic continuation to real values of θ. Our results are compatible with a second order phase transition, with the critical exponent of the SU(2) 1 Wess-ZuminoNovikov-Witten model, for sufficiently small values of the coupling. *

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Section: Discussionsupporting

confidence: 89%

Section: Introductionsupporting

confidence: 63%

“…Our aim is to understand the origin of the discrepancy between the results of Refs. [2,16,17] and those of Ref. [23].…”

Section: Introductionmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Critical behavior of theO(3)nonlinear sigma model with topological term atθ=πfrom numerical simulations

et al. 2012

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Topological lattice actions for the 2d XY model

Bietenholz

Bögli

Niedermayer

et al. 2013

J. High Energ. Phys.

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We consider the 2d XY Model with topological lattice actions, which are invariant against small deformations of the field configuration. These actions constrain the angle between neighbouring spins by an upper bound, or they explicitly suppress vortices (and anti-vortices). Although topological actions do not have a classical limit, they still lead to the universal behaviour of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition -at least up to moderate vortex suppression. Thus our study underscores the robustness of universality, which persists even when basic principles of classical physics are violated. In the massive phase, the analytically known Step Scaling Function (SSF) is reproduced in numerical simulations. In the massless phase, the BKT value of the critical exponent η c is confirmed. Hence, even though for some topological actions vortices cost zero energy, they still drive the standard BKT transition. In addition we identify a vortex-free transition point, which deviates from the BKT behaviour.

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An improved single-plaquette gauge action

Banerjee

Bögli

Holland

et al. 2016

J. High Energ. Phys.

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Abstract:We describe and test a nonperturbatively improved single-plaquette lattice action for 4-d SU(2) and SU(3) pure gauge theory, which suppresses large fluctuations of the plaquette, without requiring the naive continuum limit for smooth fields. We tune the action parameters based on torelon masses in moderate cubic physical volumes, and investigate the size of cut-off effects in other physical quantities, including torelon masses in asymmetric spatial volumes, the static quark potential, and gradient flow observables. In 2-d O(N ) models similarly constructed nearest-neighbor actions have led to a drastic reduction of cut-off effects, down to the permille level, in a wide variety of physical quantities. In the gauge theories, we find significant reduction of lattice artifacts, and for some observables, the coarsest lattice result is very close to the continuum value. We estimate an improvement factor of 40 compared to using the Wilson gauge action to achieve the same statistical accuracy and suppression of cut-off effects.

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Non-trivial θ-vacuum effects in the 2-d O(3) model

Cited by 25 publications

References 48 publications

Critical behavior of theO(3)nonlinear sigma model with topological term atθ=πfrom numerical simulations

Critical behavior of theO(3)nonlinear sigma model with topological term atθ=πfrom numerical simulations

Topological lattice actions for the 2d XY model

An improved single-plaquette gauge action

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