Finite size scaling analysis of SU(2) lattice gauge theory in (3 + 1) dimensions

Engels, Jürgen; Fingberg, Jochen; Weber, Michael

doi:10.1016/0550-3213(90)90010-b

Cited by 100 publications

(132 citation statements)

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“…and we expect therefore Z~ to have the FSS behaviour of the susceptibility [ 1 ] for T< Tc In No with slope y/v, whereas for x~ 0 the N~-behaviour is drastically changed due to the presence of xN1/~-terms ( 1/u~ 1.59 [ 8 ] ). We shall take advantage of this fact to determine the critical point as that fl-value where a linear fit ofln Z~ as a function ofln No has the least minimal X2 and/or highest goodness of fit.…”

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confidence: 99%

“…[ 1,3 ], apart from one new point. Though these data were taken at many (except on the largest lattice) fl-values in the neighbourhood of the critical point this is not sufficient for a systematic search for the asymptotic critical point.…”

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confidence: 99%

“…Finite size scaling (FSS) techniques have now become a well-established tool for the investigation of critical properties in SU (2) [1][2][3] and SU(3) [4][5][6] lattice gauge theories at finite temperature. Many ingenious methods have been devised using FSS theory to extract the infinite volume critical point and ratios of critical exponents from various variables.…”

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confidence: 99%

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Efficient calculation of critical parameters in SU (2) gauge theory

Engels

Fingerg

Mitrjushkin³

1993

Physics Letters B

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We show how the critical point and the ratio ~,/u of critical exponents of the finite temperature deconfinement transition of SU (2) gauge theory may be determined simply from the expectation value of the square of the Polyakov loop. In a similar way we estimate the ratio (a-1 )/~. The method is based on a consistent application of finite size scaling theory to results obtained with the density of states technique. It may also be used in other lattice theories at second order transitions.Finite size scaling (FSS) techniques have now become a well-established tool for the investigation of critical properties in SU(2) [1][2][3] and SU(3) [4][5][6] lattice gauge theories at finite temperature. Many ingenious methods have been devised using FSS theory to extract the infinite volume critical point and ratios of critical exponents from various variables. Most of these methods were invented in statistical physics and applied to high precision Monte Carlo data of Ising [7,8] and other comparatively simple models. Especially Binder's fourth-order cumulant [9] of the magnetization or the energy has become a favourite observable for the determination of the critical point. Besides that the peak positions of thermodynamic derivatives provide finite lattice transition points, which may be extrapolated by FSS formulas to the asymptotic critical point.Both the cumulant and the susceptibility, which are the most used observables for this purpose are quantities, which involve differences of powers of directly measured observables and require thus higher statistics to reach the same accuracy. Moreover, instead of the true susceptibility a pseudosusceptibility is commonly used, where the expectation value of the magWork supported by the Deutsche Forschungsgemeinschaft. Permanent address: Joint Institute for Nuclear Research, 101 000 Dubna, Russian Federation. netization is replaced by the one of the modulus of the magnetization.In this letter we want to show that the FSS behaviour of the expectation value of the square of the magnetization, though it is not peaked at the transition, allows to determine the asymptotic critical point and the ratio of the critical exponents 7 and u.We apply our idea to SU(2) gauge theory on N3XN~, N~=4 lattices using the standard Wilsonwhere Up is the product of link operators around a plaquette. The number of lattice points in the space (time) direction N~(~) and the lattice spacing a fix the volume and temperature asOn an infinite volume lattice the order parameter of magnetization for the deconfinement transition is the expectation value of the Polyakov loop

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Efficient calculation of critical parameters in SU (2) gauge theory

Engels

Fingerg

Mitrjushkin³

1993

Physics Letters B

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“…We used 100 independent configurations for each value of the gauge coupling, which ranges from β = 2.2 to β = 2.5. The SU (2) gauge theory has the second-order phase transition at β ≈ 2.30 for this lattice geometry [17].…”

Section: Static Hedgehog Lines From Lattice Simulationsmentioning

confidence: 99%

“…7) is very weak. For example, at β = 2.33 corresponding to the deconfinement phase, for one of the densities, the values ρ + = 0.0427 (17), 0.0455(29), and 0.0468(41), correspond to the respective bin numbers N L = 100, 200, and 300. A similar weak dependence on the number of bins is observed for ρ − .…”

Section: Static Hedgehog Lines From Lattice Simulationsmentioning

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Hedgehogs in Wilson loops and phase transition in SU(2) Yang–Mills theory

2006

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We suggest that the gauge-invariant hedgehoglike structures in the Wilson loops are physically interesting degrees of freedom in the Yang-Mills theory. The trajectories of these "hedgehog loops" are closed curves corresponding to center-valued (untraced) Wilson loops and are characterized by the center charge and winding number. We show numerically in the SU(2) Yang-Mills theory that the density of hedgehog structures in the thermal Wilson-Polyakov line is very sensitive to the finite-temperature phase transition. The (additively normalized) hedgehog line density behaves like an order parameter: the density is almost independent of the temperature in the confinement phase and changes substantially as the system enters the deconfinement phase. In particular, our results suggest that the (static) hedgehog lines may be relevant degrees of freedom around the deconfinement transition and thus affect evolution of the quark-gluon plasma in high-energy heavy-ion collisions.

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Recent Results from Lattice QCD

Fingberg

1994

NATO ASI Series

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Finite size scaling analysis of SU(2) lattice gauge theory in (3 + 1) dimensions

Cited by 100 publications

References 13 publications

Efficient calculation of critical parameters in SU (2) gauge theory

Efficient calculation of critical parameters in SU (2) gauge theory

Hedgehogs in Wilson loops and phase transition in SU(2) Yang–Mills theory

Recent Results from Lattice QCD

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