Monte-Carlo simulation of pure U(N) and SU(N) lattice gauge theories with fundamental and adjoint couplings

Ardill, R.W.B.; Moriarty, K.J.M.; Creutz, Michael

doi:10.1016/0010-4655(83)90030-9

Cited by 24 publications

(3 citation statements)

References 28 publications

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“…The Z 2 monopole density should vanish in the continuum limit g 2 → 0. This happens, however, in different ways, depending on the dimensions d or the direction along which such limit is taken in the β F − β A plane, and has been the subject of intense investigations in the pioneering years of lattice gauge theories [38,[42][43][44][45][46][48][49][50][51][52][53][54]. For the SU (2) − SO (3) case considered here the resulting phase diagrams in d = 3 and 4 are sketched in Figs theory has no phase transition; apart from the roughening transition [48], the corresponding phase diagram should therefore be free of any bulk effects, including crossovers.…”

Section: A Action and Observablesmentioning

confidence: 99%

“…where a is the (dimensionful) lattice spacing and U P denotes the 1 × 1 plaquette; all results can be easily generalized to different boundary conditions. For higher groups SU (N ) the general picture should not change dramatically [29,[42][43][44][45][46]. However, other representations than just the fundamental and adjoint are allowed.…”

Section: Setup a Action And Observablesmentioning

confidence: 99%

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Topological order and the vacuum of Yang-Mills theories

Burgio

Reinhardt

2015

Phys. Rev. D

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We study, for $SU(2)$ Yang-Mills theories discretized on a lattice, a non-local topological order parameter, the center flux ${{z}}$. We show that: i) well defined topological sectors classified by $\pi_1(SO(3))=\mathbb{Z}_2$ can only exist in the ordered phase of ${{z}}$; ii) depending on the dimension $2 \leq d\leq 4$ and action chosen, the center flux exhibits a critical behaviour sharing striking features with the Kosterlitz-Thouless type of transitions, although belonging to a novel universality class; iii) such critical behaviour does not depend on the temperature $T$. Yang-Mills theories can thus exist in two different continuum phases, characterized by an either topologically ordered or disordered vacuum; this reminds of a quantum phase transition, albeit controlled by the choice of symmetries and not by a physical parameter.Comment: 32 pages, 15 figures. Typos corrected; to appear on PR

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Section: A Action and Observablesmentioning

confidence: 99%

Section: Setup a Action And Observablesmentioning

confidence: 99%

Topological order and the vacuum of Yang-Mills theories

Burgio

Reinhardt

2015

Phys. Rev. D

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“…This has led to a substantial reduction of cut-off effects in a variety of asymptotically free field theories, ranging from the 2-d O(3) model to QCD. A different approach uses mixed fundamental-adjoint actions to reduce cut-off effects without extending the space-time extent of the operators beyond a single plaquette, and thus with only a moderate increase of the computational cost [10][11][12][13]. In [14,15] the…”

Section: Introductionmentioning

confidence: 99%

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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Density ofZ(3) flux loops inSU(3) lattice gauge theory in four dimensions

Bunk

Moriarty

1984

Z. Phys. C - Particles and Fields

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Monte-Carlo simulation of pure U(N) and SU(N) lattice gauge theories with fundamental and adjoint couplings

Cited by 24 publications

References 28 publications

Topological order and the vacuum of Yang-Mills theories

Topological order and the vacuum of Yang-Mills theories

An improved single-plaquette gauge action

Density ofZ(3) flux loops inSU(3) lattice gauge theory in four dimensions

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