B. Petersson

Bielefeld University, Bielefeld, North Rhine-Westphalia, Germany

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Publications (109)311.24 Total impact

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    ABSTRACT: We have measured the correlation function of Polyakov loops on the lattice in three dimensional SU(3) gauge theory near its finite temperature phase transition. Using a new and powerful application of finite size scaling, we furthermore extend the measurements of the critical couplings to considerably larger values of the lattice sizes, both in the temperature and space directions, than was investigated earlier in this theory. With the help of these measurements we perform a detailed finite size scaling analysis, showing that for the critical exponents of the two dimensional three state Potts model the mass and the susceptibility fall on unique scaling curves. This strongly supports the expectation that the gauge theory is in the same universality class. The Nambu-Goto string model on the other hand predicts that the exponent \nu has the mean field value, which is quite different from the value in the abovementioned Potts model. Using our values of the critical couplings we also determine the continuum limit of the value of the critical temperature in terms of the square root of the zero temperature string tension. This value is very near to the prediction of the Nambu-Goto string model in spite of the different critical behaviour.
    Nuclear Physics B 11/2012; 871(1). · 4.33 Impact Factor
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    ABSTRACT: Employing Monte-Carlo simulation we study the phase diagram of a Z2 gauge field coupled to simplicial quantum gravity. We localize a critical point of the model where both the matter and gravity sectors have a second order phase transition. We found the value of the critical index γg=0.16(4) of the gravity susceptibility at the critical point.
    Modern Physics Letters A 11/2011; 09(27). · 1.11 Impact Factor
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    P. Bialas, Z. Burda, B. Petersson
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    ABSTRACT: We show that the lowest part of the eigenvalue density of the staggered fermion operator in lattice QCD3 at small lattice coupling constant β has exactly the same shape as in QCD4. This observation is quite surprising, since universal properties of the QCD3 Dirac operator are expected to be described by a nonchiral matrix model. We show that this effect is related to the specific nature of the staggered fermion discretization and that the eigenvalue density evolves toward the nonchiral random matrix prediction when β is increased and the continuum limit is approached. We propose a two-matrix model with one free parameter which interpolates between the two limits and very well mimics the pattern of evolution with β of the eigenvalue density of the staggered fermion operator in QCD3.
    Physical review D: Particles and fields 01/2011; 83(1).
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    P. Bialas, L. Daniel, A. Morel, B. Petersson
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    ABSTRACT: We determine the correlation between Polyakov loops in three dimensional SU(3) gauge theory in the confined region at finite temperature. For this purpose we perform lattice calculations for the number of steps in the temperature direction equal to six. This is expected to be in the scaling region of the lattice theory. We compare the results to the bosonic string model. The agreement is very good for temperatures T<0.7T_c, where T_c is the critical temperature. In the region 0.7T_c<T<T_c we enter the critical region, where the critical properties of the correlations are fixed by universality to be those of the two dimensional three state Potts model. Nevertheless, by calculating the critical lattice coupling, we show that the ratio of the critical temperature to the square root of the zero temperature string tension, where the latter is taken from the literature, remains very near to the string model prediction. Comment: 11 pages, 1 figure, 1 table
    Nuclear Physics B 12/2009; · 4.33 Impact Factor
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    P. Bialas, L. Daniel, A. Morel, B. Petersson
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    ABSTRACT: The pressure, and the energy and entropy densities are determined for the SU(3) gauge theory in 2+1 dimensions from lattice Monte Carlo calculations in the interval 0.6⩽T/Tc⩽15. The finite temperature lattices simulated have temporal extent Nτ=2, 4, 6 and 8, and spatial volumes such that the aspect ratio is NS/Nτ=8. To obtain the thermodynamical quantities, we calculate the averages of the temporal plaquettes Pτ and the spatial plaquettes PS on these lattices. We also need the zero temperature averages of the plaquettes P0, calculated on symmetric lattices with Nτ=NS. We discuss in detail the finite size (NS-dependent) effects. These disappear exponentially. For the zero temperature lattices we find that the coefficient of NS in the exponent is of the order of the glueball mass. On the finite temperature lattices it lies between the two lowest screening masses. For the aspect ratio equal to eight, the systematic errors coming from the finite size effects are much smaller than our statistical errors. We argue that in the continuum limit, at high enough temperature, the pressure can be parametrized by the very simple formula p=T3(a−bTc/T) where a and b are two constants. Using the thermodynamical identities for a large homogeneous system, this parametrization then determines the other thermodynamical variables in the same temperature range.
    Nuclear Physics B 01/2009; · 4.33 Impact Factor
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    P. Bialas, L. Daniel, A. Morel, B. Petersson
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    ABSTRACT: In this article we will discuss numerical results on screening masses and thermodynamic quantities in 2 + 1 dimensional SU(3) gauge theory. We will also compare them to perturbation theory and the dimensionally reduced model.
    Nuclear Physics A 07/2006; · 1.53 Impact Factor
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    Zdzislaw Burda, Bengt Petersson, Marc Wattenberg
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    ABSTRACT: We investigate semiclassical properties of space-time geometry of the low energy limit of reduced four dimensional supersymmetric Yang-Mills integrals using Monte-Carlo simulations. The limit is obtained by an one-loop approximation of the original Yang-Mills integrals leading to an effective model of branched polymers. We numerically determine the behaviour of the gyration radius, the two-point correlation function and the Polyakov-line operator in the effective model and discuss the results in the context of the large-distance behaviour of the original matrix model. Comment: 14 pages, 5 figures, corrected version v3
    Journal of High Energy Physics 03/2005; · 5.62 Impact Factor
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    P. Bialas, A. Morel, B. Petersson
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    ABSTRACT: We analyze a two-dimensional SU(3) gauge model of Wilson lines as a dimensionally reduced model of high temperature QCD3. In contrast to perturbative dimensional reduction it has an explicit global Z3 symmetry in the action. The phase diagram of the model is studied in the space of two free parameters used to describe the self interaction of the Wilson lines. In addition to the confinement–deconfinement transition, the model also exhibits a new Z3-breaking phase. These findings are obtained by numerical simulations, and supported by a perturbative calculation to one loop. A screening mass from Polyakov loop correlations is calculated numerically. It matches the known QCD3 mass in a domain of parameters belonging to the normal deconfined phase.
    Nuclear Physics B 01/2005; 704(1):208-230. · 4.33 Impact Factor
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    P. Bialas, A. Morel, B. Petersson
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    ABSTRACT: In this contribution we present the results of a series of investigations of dimensional reduction, applied to SU(3) gauge theory in 2 + 1 dimensions. We review earlier results, present a new reduced model with Z(3) symmetry, and discuss the results of numerical simulations of this model.
    Progress of Theoretical Physics Supplement 04/2004; · 1.25 Impact Factor
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    P. Bialas, A. Morel, B. Petersson
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    ABSTRACT: We present first results from a numerical investigation of a Z(3) symmetric model based on dimensional reduction. Comment: Talk presented at XXI International Symposium on Lattice Field Theory lattice2003(Non-zero temperature and density)
    Nuclear Physics B - Proceedings Supplements 09/2003; · 0.88 Impact Factor
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    Zdzislaw Burda, Bengt Petersson, Marc Wattenberg
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    ABSTRACT: We derive analytically one-loop corrections to the effective Polyakov-line operator in the branched-polymer approximation of the reduced four-dimensional supersymmetric Yang-Mills integrals.
    Acta Physica Polonica Series B 09/2003; · 1.01 Impact Factor
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    Z Burda, J Erdmann, B Petersson, M Wattenberg
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    ABSTRACT: We discuss the scaling properties of free branched polymers. The scaling behavior of the model is classified by the Hausdorff dimensions for the internal geometry, d(L) and d(H), and for the external one, D(L) and D(H). The dimensions d(H) and D(H) characterize the behavior for long distances, while d(L) and D(L) for short distances. We show that the internal Hausdorff dimension is d(L)=2 for generic and scale-free trees, contrary to d(H), which is known to be equal to 2 for generic trees and to vary between 2 and infinity for scale-free trees. We show that the external Hausdorff dimension D(H) is directly related to the internal one as D(H)=alphad(H), where alpha is the stability index of the embedding weights for the nearest-vertex interactions. The index is alpha=2 for weights from the Gaussian domain of attraction and 0<alpha<2 for those from the Lévy domain of attraction. If the dimension D of the target space is larger than D(H), one finds D(L)=D(H), or otherwise D(L)=D. The latter result means that the fractal structure cannot develop in a target space that has too low dimension.
    Physical Review E 02/2003; 67(2 Pt 2):026105. · 2.31 Impact Factor
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    P. Bialas, A. Morel, B. Petersson, K. Petrov
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    ABSTRACT: Here we present a candidate for a Z(3)-symmetric reduced action for the description of the (2+1)D SU(3) gauge theory
    01/2002;
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    P. Bialas, A. Morel, B. Petersson, K. Petrov
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    ABSTRACT: We discuss the screening masses and residue factorisation of the SU(3) (2+1)D theory in the dimensional reduction formalism. The phase structure of the reduced model is also investigated.
    Nuclear Physics B - Proceedings Supplements 11/2001; · 0.88 Impact Factor
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    ABSTRACT: Lattice formulation of a fermionic field theory defined on a randomly triangulated compact manifold is discussed, with emphasis on the topological problem of defining spin structures on the manifold. An explicit construction is presented for the two-dimensional case and its relation with the Ising model is discussed. Furthermore, an exact realization of the Kramers-Wannier duality for the two-dimensional Ising model on the manifold is considered. The global properties of the field are discussed. The importance of the GSO projection is stressed. This projection has to be performed for the duality to hold.
    Acta Physica Polonica Series B 11/2001; · 1.01 Impact Factor
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    L. Bogacz, Z. Burda, C. Petersen, B. Petersson
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    ABSTRACT: We implement fermions on dynamical random triangulation and determine numerically the spectrum of the Dirac-Wilson operator D for the system of Majorana fermions coupled to two-dimensional Euclidean quantum gravity. We study the dependence of the spectrum of the operator (epsilon D) on the hopping parameter. We find that the distributions of the lowest eigenvalues become discrete when the hopping parameter approaches the value 1/sqrt{3}. We show that this phenomenon is related to the behavior of the system in the 'antiferromagnetic' phase of the corresponding Ising model. Using finite size analysis we determine critical exponents controlling the scaling of the lowest eigenvalue of the spectrum including the Hausdorff dimension d_H and the exponent kappa which tells us how fast the pseudo-critical value of the hopping parameter approaches its infinite volume limit. Comment: 26 pages, Latex + 23 eps figs, extended analysis of the spectrum, added figures
    Nuclear Physics B 07/2001; · 4.33 Impact Factor
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    ABSTRACT: We present a numerical study of an SU(3) gauged 2D model for adjoint scalar fields, defined by dimensional reduction of pure gauge QCD in (2+1)D at high temperature. We show that the correlations between Polyakov loops are saturated by two colourless bound states, respectively, even and odd under the Z2 symmetry related to time reversal in the original theory. Their contributions (poles) in correlation functions of local composite operators An, respectively, of degree n=2p and 2p+1 in the scalar fields (p=1,2) fulfill factorization. The contributions of two particle states (cuts) are detected. Their size agrees with estimates based on a meanfield-like decomposition of the p=2 operators into polynomials in p=1 operators. In contrast to the naive picture of Debye screening, no sizable signal in any An correlation can be attributed to 1/n times a Debye screening length associated with n elementary fields. These results are quantitatively consistent with the picture of scalar “matter” fields confined within colourless boundstates whose residual “strong” interactions are very weak.
    Nuclear Physics B 01/2001; · 4.33 Impact Factor
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    Z. Burda, B. Petersson, J. Tabaczek
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    ABSTRACT: We study numerically the geometric properties of reduced supersymmetric non-compact SU(N) Yang–Mills integrals in D=4 dimensions, for N=2,3,…,8. We show that in the range of large eigenvalues of the matrices Aμ, the original D-dimensional rotational symmetry is spontaneously broken and the dominating field configurations become one-dimensional, as anticipated by studies of the underlying surface theory. We also discuss possible implications of our results for the IKKT model.
    Nuclear Physics B 01/2001; · 4.33 Impact Factor
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    Bengt Petersson
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    ABSTRACT: In this talk I will first give a short discussion of some lattice results for QCD at finite temperature. I will then describe in some detail the technique of dimensional reduction, which in principle is a powerful technique to obtain results on the long distance properties of the quark-gluon plasma. Finally I will describe some new results, which test the technique in a simpler model, namely three dimensional gauge theory.
    10/2000;
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    P. Bialas, Z. Burda, B. Petersson, J. Tabaczek
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    ABSTRACT: Using the dynamical triangulation approach we perform a numerical study of a supersymmetric random surface model that corresponds to the large N limit of the four-dimensional version of the IKKT matrix model. We show that the addition of fermionic degrees of freedom suppresses the spiky world-sheet configurations that are responsible for the pathological behaviour of the purely bosonic model. We observe that the distribution of the gyration radius has a power-like tail p(R) ~ R^{-2.4}. We check numerically that when the number of fermionic degrees of freedom is not susy-balanced, p(R) grows with $R$ and the model is not well-defined. Numerical sampling of the configurations in the tail of the distribution shows that the bosonic degrees of freedom collapse to a one-dimensional tube with small transverse fluctuations. Assuming that the vertex positions can fluctuate independently within the tube, we give a theoretical argument which essentially explains the behaviour of p(R) in the different cases, in particular predicting p(R) ~ R^{-3} in the supersymmetric case. Extending the argument to six and ten dimensions, we predict p(R) ~ R^{-7} and p(R) ~ R^{-15}, respectively.
    Nuclear Physics B 08/2000; · 4.33 Impact Factor