The phase structure of SU(N)/Z(N) lattice gauge theories

Halliday, I.G.; Schwimmer, A.

doi:10.1016/0370-2693(81)90055-1

Cited by 114 publications

(57 citation statements)

References 13 publications

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“…Such transitions are almost independent of the size of the lattice and are driven by lattice artifacts [20]. Bulk transitions between the unphysical strong-coupling and the physical weak-coupling regimes in lattice gauge theories is the rule rather than the exception.…”

Section: The Bulk Transitionmentioning

confidence: 99%

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Phase diagram of the latticeG2Higgs model

Wellegehausen

Wipf²,

Wozar³

2011

Phys. Rev. D

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We study the phases and phase transition lines of the finite temperature G2 Higgs model. Our work is based on an efficient local hybrid Monte-Carlo algorithm which allows for accurate measurements of expectation values, histograms and susceptibilities. On smaller lattices we calculate the phase diagram in terms of the inverse gauge coupling β and the hopping parameter κ. For κ → 0 the model reduces to G2 gluodynamics and for κ → ∞ to SU (3) gluodynamics. In both limits the system shows a first order confinement-deconfinement transition. We show that the first order transitions at asymptotic values of the hopping parameter are almost joined by a line of first order transitions. A careful analysis reveals that there exists a small gap in the line where the first order transitions turn into continuous transitions or a cross-over region. For β → ∞ the gauge degrees of freedom are frozen and one finds a nonlinear O(7) sigma model which exhibits a second order transition from a massive O(7)-symmetric to a massless O(6)-symmetric phase. The corresponding second order line for large β remains second order for intermediate β until it comes close to the gap between the two first order lines. Besides this second order line and the first order confinement-deconfinement transitions we find a line of monopole-driven bulk transitions which do not interfer with the confinement-deconfinment transitions.

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Section: The Bulk Transitionmentioning

confidence: 99%

“…There is ample evidence that bulk transitions are driven by monopoles on the lattice [20]. Thus we calculated the density of monopoles [24] as a function of β for κ = 0 and κ = 1.8.…”

Section: The Bulk Transitionmentioning

confidence: 99%

Phase diagram of the latticeG2Higgs model

Wellegehausen

Wipf²,

Wozar³

2011

Phys. Rev. D

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“…1 shows the common picture as obtained in [4,20] for d = 2, 3. Order parameters for the transitions/crossovers (except for the roughening one [21]) are Z 2 magnetic monopole σ c and electric vortices σ l densities M and E [5,6]:…”

Section: Action and Observablesmentioning

confidence: 99%

“…In 3+1 dimensions the theories exhibit in the β A -β F phase diagram bulk transitions [3,4] (see Fig. 1) related to the condensation of Z N magnetic monopoles σ c and electric vortices σ l [5,6].…”

Section: Introductionmentioning

confidence: 99%

Vortex topology and the continuum limit of lattice gauge theories

Burgio¹

2008

Proceedings of the XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007)

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We study the stability of Z 2 topological vortex excitations in d+1 dimensional SU(2) Yang-Mills theory on the lattice at T = 0. This is found to depend on d and on the coupling considered. We discuss the connection with lattice artifacts causing bulk transitions in the β A -β F plane and draw some conclusions regarding the continuum limit of the theory.The XXV International Symposium on Lattice Field Theory

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“…The above condition is usually quoted when claiming that the bulk transition separating the strong and weak coupling regime along β A [11,12,13,14,15] constitutes an obstacle in defining the continuum limit for the adjoint Wilson action. This however assumes that topological sectors along the fundamental coupling β are always well defined.…”

Section: Introductionmentioning

confidence: 99%