Generalized Potts-Models and their Relevance for Gauge Theories

Wipf, Andreas

doi:10.3842/sigma.2007.006

Cited by 4 publications

(4 citation statements)

References 24 publications

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“…Near the transition point its dynamics is successfully described by effective three dimensional scalar field models for the characters of P( x) [1][2][3]. If one further projects the Polyakov loops onto the center of the gauge group, then one arrives at generalized Potts models describing the effective Polyakov-loop dynamics [4]. With matter in the fundamental representation the center symmetry is explicitly broken and for all temperatures has P a nonzero expectation value and points in the direction of a particular center element.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Phase diagram of the latticeG2Higgs model

Wellegehausen

Wipf²,

Wozar³

2011

Phys. Rev. D

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“…7 shows the logarithm of the glue-lump correlator (51) as function of the separation of the two lumps for static charges in the fundamental representations 7 and 14. The linear fits to the data yield the glue-lump masses m 7 = 0.46(4), m 14 = 0.767 (5).…”

Section: String Breaking and Glue-lumps In 3 Dimensionsmentioning

confidence: 92%

“…In the vicinity of the transition point the dynamics of the Polyakov loop is successfully described by effective 3d scalar field models for the characters of the Polyakov loop [1][2][3][4]. If one further projects the scalar fields onto the center of the gauge group then one arrives at generalized Potts models describing the effective Polyakov-loop dynamics [5]. The temperature dependent couplings constants of these effective theories have been calculated ab initio by inverse Monte Carlo methods in [3].…”

Section: Introductionmentioning

confidence: 99%

Casimir scaling and string breaking inG2gluodynamics

Wellegehausen

Wipf²,

Wozar

2011

Phys. Rev. D

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We study the potential energy between static charges in G 2 gluodynamics in three and four dimensions. Our work is based on an efficient local hybrid Monte Carlo algorithm and a multilevel Lüscher-Weisz algorithm with exponential error reduction to accurately measure expectation values of Wilson and Polyakov loops. Both in three and four dimensions we show that at intermediate scales the string tensions for charges in various G 2 representations scale with the second order Casimir. In three dimensions Casimir scaling is confirmed within 4% for charges in representations of dimensions 7, 14, 27, 64, 77, 77 0 , 182, and 189 and in four dimensions within 5% for charges in representations of dimensions 7, 14, 27, and 64. In three dimensions we detect string breaking for charges in the two fundamental representations. The scale for string breaking agrees very well with the mass of the created pair of glue lumps. Close to the string breaking distance Casimir scaling between adjoint and defining representation is violated by 2.5%. The analytical prediction for the continuum string tension is confirmed for the defining representation in three dimensions.

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Section: Introductionmentioning

confidence: 99%

Phase diagram of the G(2) Higgs model

Wellegehausen¹

2012

Proceedings of XXIX International Symposium on Lattice Field Theory — PoS(Lattice 2011)

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We investigate gauge theories based on the smallest exceptional simple lie group G 2 . Our first model considered here is G 2 Yang-Mills coupled to a fundamental Higgs field. In 4 spacetime dimensions we explore the phase diagram of the theory, showing that at larger Higgs masses the first order deconfinement phase transition turns into a crossover and therefore connects the low temperature confined phase with the high temperature deconfined phase. The second model investigated is G 2 Yang-Mills coupled to fundamental fermions. It shares many features with QCD, especially fermionic baryons, but due to the absence of the fermion sign problem we can investigate this theory with Monte Carlo techniques even at low temperature and high baryonic density. First results on small lattices are presented.

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Generalized Potts-Models and their Relevance for Gauge Theories

Cited by 4 publications

References 24 publications

Phase diagram of the latticeG2Higgs model

Phase diagram of the latticeG2Higgs model

Casimir scaling and string breaking inG2gluodynamics

Phase diagram of the G(2) Higgs model

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