6,196 research outputs found

    The analysis of Polyakov loop and spin correlators in finite volumes

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    We derive an analytic expression for point to point correlation functions of the Polyakov loop based on the transfer matrix formalism. The contributions from the eigenvalues of the transfer matrix including and beyond the mass gap are investigated both for the 2d2d Ising model and in finite temperature SU(2)SU(2) gauge theory. We find that the leading matrix element shows similar scaling properties in both models. Just above the critical point we obtain for SU(2)SU(2) a Debye screening mass  μD/T≈4 ~\mu_D/T\approx4~, independent of the volume. Sorry, figures are not included and can be sent by ordinary mail.Comment: TALK GIVEN AT THE LATTICE '93 INTERNATIONAL SYMPOSIUM LATTICE FIELD THEORY, DALLAS, USA, OCTOBER 12--16, 1993 3 pages preprint HU BERLIN--IEP--93/5 and BIELEFELD BI-TP--93/63, November 199

    Comparison of finite-size-scaling functions for 3d O(N) spin models to QCD

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    We calculate numerically universal finite-size-scaling functions of the magnetization for the three-dimensional O(4) and O(2) spin models. The approach of these functions to the infinite-volume scaling functions is studied in detail on the critical and pseudocritical lines. For this purpose we determine the pseudocritical line in two different ways. We find that the asymptotic form of the finite-size-scaling functions is already reached at small values of the scaling variable. A comparison with QCD lattice data for two flavours of staggered fermions shows a similar finite-size behaviour which is compatible with that of the spin models.Comment: Lattice2001(hightemp), 3 pages, 5 figures, acknowledgements completed, minor typographical errors correcte

    Corrections to Scaling and Critical Amplitudes in SU(2) Lattice Gauge Theory

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    We calculate the critical amplitudes of the Polyakov loop and its susceptibility at the deconfinement transition of SU(2) gauge theory. To this end we carefully study the corrections to the scaling functions of the observables coming from irrelevant exponents. As a guiding line for determining the critical amplitudes we use envelope equations derived from the finite size scaling formulae for the observables. The equations are then evaluated with new high precision data obtained on N^3 x 4 lattices for N=12,18,26 and 36. We find different correction-to-scaling behaviours above and below the transition. Our result for the universal ratio of the susceptibility amplitudes is C_+/C_-=4.72(11) and agrees perfectly with a recent measurement for the 3d Ising model.Comment: LATTICE98(hightemp

    The Pseudo Specific Heat in SU(2) Gauge Theory : Finite Size Dependence and Finite Temperature Effects

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    We investigate the pseudo specific heat of SU(2) gauge theory near the crossover point on 444^4 to 16416^4 lattices. Several different methods are used to determine the specific heat. The curious finite size dependence of the peak maximum is explained from the interplay of the crossover phenomenon with the deconfinement transition occurring due to the finite extension of the lattice. We find, that for lattices of size 848^4 and larger the crossover peak is independent of lattice size at βco=2.23(2)\beta_{co}=2.23(2) and has a peak height of CV,co=1.685(10)C_{V,co}=1.685(10). We conclude therefore that the crossover peak is not the result of an ordinary phase transition. Further, the contributions to CVC_V from different plaquette correlations are calculated. We find, that at the peak and far outside the peak the ratio of contributions from orthogonal and parallel plaquette correlations is different. To estimate the finite temperature influence on symmetric lattices far off the deconfinement transition point we calculate the modulus of the lattice average of the Polyakov loop on these lattices and compare it to predictions from a random walk model.Comment: Latex 2e,10 pages including 5 postscript figure

    Finite size analysis of the pseudo specific heat in SU(2) gauge theory

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    We investigate the pseudo specific heat of SU(2) gauge theory near the crossover point on 444^4 to 16416^4 lattices. Several different methods are used to determine the specific heat. The curious finite size dependence of the peak maximum is explained from the interplay of the crossover phenomenon with the deconfinement transition occurring due to the finite extension of the lattice. In this context we calculate the modulus of the lattice average of the Polyakov loop on symmetric lattices and compare it to the prediction from a random walk model.Comment: Talk presented at LATTICE96(finite temperature), 3 pages, 4 Postscript figure

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

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    We determine the critical point and the ratios β/ν\beta/\nu and γ/ν\gamma/\nu of critical exponents of the deconfinement transition in SU(2)SU(2) gauge theory by applying the χ2\chi^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 grg_r its universal value at the critical point in the thermodynamical limit to −1.403(16)-1.403(16) and for the next-to-leading exponent ω=1±0.1\omega=1\pm0.1. From the derivatives of the Polyakov loop dependent quantities we estimate then 1/ν1/\nu. The result from the derivative of grg_r is 1/ν=0.63±0.011/\nu=0.63\pm0.01, in complete agreement with that of the 3d3d Ising model.Comment: 11 pages, 3 Postscript figures, uses Plain Te

    Non-perturbative determination of anisotropy coefficients in lattice gauge theories

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    We propose a new non-perturbative method to compute derivatives of gauge coupling constants with respect to anisotropic lattice spacings (anisotropy coefficients), which are required in an evaluation of thermodynamic quantities from numerical simulations on the lattice. Our method is based on a precise measurement of the finite temperature deconfining transition curve in the lattice coupling parameter space extended to anisotropic lattices by applying the spectral density method. We test the method for the cases of SU(2) and SU(3) gauge theories at the deconfining transition point on lattices with the lattice size in the time direction Nt=4N_t=4 -- 6. In both cases, there is a clear discrepancy between our results and perturbative values. A longstanding problem, when one uses the perturbative anisotropy coefficients, is a non-vanishing pressure gap at the deconfining transition point in the SU(3) gauge theory. Using our non-perturbative anisotropy coefficients, we find that this problem is completely resolved: we obtain Δp/T4=0.001(15)\Delta p/T^4 = 0.001(15) and −0.003(17)-0.003(17) on Nt=4N_t=4 and 6 lattices, respectively.Comment: 24pages,7figures,5table

    Longitudinal and transverse spectral functions in the three-dimensional O(4) model

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    We have performed a high statistics simulation of the O(4) model on a three-dimensional lattice of linear extension L=120 for small external fields H. Using the maximum entropy method we analyze the longitudinal and transverse plane spin correlation functions for T=T_c. In the transverse case we find for all T and H a single sharp peak in the spectral function, whose position defines the transverse mass m_T, the correlator is that of a free particle with mass m_T. In the longitudinal case we find in the very high temperature region also a single sharp peak in the spectrum. On approaching the critical point from above the peak broadens somewhat and at T_c its position m_L is at 2m_T for all our H-values. Below T_c we find still a significant peak at omega=2m_T and at higher omega-values a continuum of states with several smaller peaks with decreasing heights. This finding is in accord with a relation of Patashinskii and Pokrovskii between the longitudinal and the transverse correlation functions. We test this relation in the following. As a by-product we calculate critical exponents and amplitudes and confirm our former results.Comment: 38 pages, 26 figure

    Numerical equation of state and other scaling functions from an improved three-dimensional Ising model

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    We study an improved three-dimensional Ising model with external magnetic field near the critical point by Monte Carlo simulations. From our data we determine numerically the universal scaling functions of the magnetization, that is the equation of state, of the susceptibility and of the correlation length. In order to normalize the scaling functions we calculate the critical amplitudes of the three observables on the critical line, the phase boundary and the critical isochore. These amplitudes lead to the universal ratios C^+/C^-=4.756(28), R_{chi}=1.723(13), Q_c=0.326(3) and Q_2=1.201(10). We find excellent agreement of the data with the parametric representation of the asymptotic equation of state as found by field theory methods. The comparison of the susceptibility data to the corresponding scaling function shows a marginal difference in the symmetric phase, which can be explained by the slightly different value for R_{chi} used in the parametrization. The shape of the correlation-length-scaling function is similar to the one of the susceptibility, as expected from earlier parametrizations. The peak positions of the two scaling functions are coinciding within the error bars.Comment: 27 pages, 14 Ps-figures, Latex2e, 10 pages added, including the scaling function of the correlation length, to appear in Nucl. Phys.
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