Phenomenological renormalization and scaling behaviour of SU(2) lattice gauge theory

Engels, Jürgen; Fingberg, Jochen; Miller, David

doi:10.1016/0550-3213(92)90171-7

Cited by 57 publications

(69 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Indeed it is in excellent agreement with the best determination from the cumulant [ 3 ] flc,~=2.2986(6),…”

supporting

confidence: 73%

“…[ 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.…”

mentioning

confidence: 99%

“…Following the same lines as in ref. [3], we have reevaluated the data in the very close vicinity (2.2980~<fl~<2.3005) of the transition. In fig.…”

mentioning

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.…”

mentioning

confidence: 99%

“…There only four overlapping histograms were available from refs. [ 1,3 ]. To improve this situation and to test the stability of the DSM interpolation we calculated one new point at fl= 2.2988 on the 263 X 4 lattice with a 9 times higher statistics as compared to the point at fl= 2.30.…”

mentioning

confidence: 99%

See 4 more Smart Citations

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

Engels

Fingerg

Mitrjushkin³

1993

Physics Letters B

Self Cite

View full text Add to dashboard Cite

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

show abstract

“…Indeed it is in excellent agreement with the best determination from the cumulant [ 3 ] flc,~=2.2986(6),…”

supporting

confidence: 73%

mentioning

confidence: 99%

“…Following the same lines as in ref. [3], we have reevaluated the data in the very close vicinity (2.2980~<fl~<2.3005) of the transition. In fig.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

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

Engels

Fingerg

Mitrjushkin³

1993

Physics Letters B

Self Cite

View full text Add to dashboard Cite

show abstract

Finite-size scaling behaviour of the SU(2) lattice gauge theory

Alves

1994

Physics Letters B

View full text Add to dashboard Cite

Critical behaviour of SU(2) lattice gauge theory. A complete analysis with the χ2-method

et al. 1996

Self Cite

View full text Add to dashboard Cite

We determine the critical point and the ratios β/ν and γ/ν of critical exponents of the deconfinement transition in SU (2) gauge theory by applying the χ 2 -method to Monte Carlo data of the modulus and the square of the Polyakov loop. With the same technique we find from the Binder cumulant g r its universal value at the critical point in the thermodynamical limit to −1.403(16) and for the next-to-leading exponent ω = 1 ± 0.1. From the derivatives of the Polyakov loop dependent quantities we estimate then 1/ν. The result from the derivative of g r is 1/ν = 0.63 ± 0.01, in complete agreement with that of the 3d Ising model.

show abstract

Phenomenological renormalization and scaling behaviour of SU(2) lattice gauge theory

Cited by 57 publications

References 17 publications

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

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

Finite-size scaling behaviour of the SU(2) lattice gauge theory

Critical behaviour of SU(2) lattice gauge theory. A complete analysis with the χ2-method

Contact Info

Product

Resources

About