Discussion of thermodynamic features within the PNJL model

We discuss some thermodynamical features of a QCD system within the two-flavor Polyakov loop extended Nambu–Jona-Lasinio(PNJL) model. Several thermodynamical quantities of interest(pressure, energy density,specific heat, speed of sound, etc.) are investigated and discussed in detail with two different forms of Polyakov loop potential. The effective coupling strength G incorporating a quark feedback(quark condensate) through operator product expansion is also discussed, as well as the relationship between color deconfinement and chiral phase crossover.We find that some thermodynamical quantities have quite different behavior for different Polyakov loop potentials.By changing the characteristic temperature T_0 of the pure Yang-Mills field, we find that when T_0 becomes small,color deconfinement might happen earlier than chiral phase crossover, while their relationship can be determined via some thermodynamical quantities. Furthermore, the behavior of the thermodynamical quantities is quite different in the two different forms of Polyakov loop potential studied. Especially, one of the potentials, specific heat, has two peaks, which correspond to color deconfinement and chiral phase crossover respectively. This interesting phenomenon may shed some light on whether the inflection points of the chiral condensate and deconfinement transitions happen at the same temperature or not for lattice QCD and experimental studies.     

Solutions of Polyakov's loop equations and their contribution to loop averages

The solutions of the classical equations for the Wilson loop presented by Polyakov are studied forU(1) andSU(2) gauge theories on a lattice. All the solutions are found ford=2 space-time dimensions while a particular set is obtained ford-3,4. A possible application of this result to the computation of quantum loop averages in the weak coupling region is discussed: ind=2 a saddle point approximation is shown to be very accurate and simple in terms of loop variables.     

Polyakov loop distributions near deconfinement inSU(2) lattice gauge theory

The distribution function of the Polyakov loop is investigated on a 16³×3 lattice in the neighbourhood of the deconfinement transition ofSU(2) gauge theory. We find, that well above the transition the distribution is a Gaussian; when the coupling approaches the critical point it is modified due to phase flip attempts of the system. Corresponding distributions for the plaquettes remain, however, Gaussian. For one coupling close to the transition we study the distributions on 8³, 12³ and 18³×4 lattices and show that strong finite size effects are present. Using the maximum values of the Gaussian parts of the distributions we construct a more physical (and therefore scaling) order parameter whose critical exponent is in excellent agreement with the universality hypothesis.     

Monte Carlo simulation of non-compact QCD with stochastic gauge fixing

A non-compact lattice model of quantum chromodynamics is studied numerically. Whereas in Wilson's lattice theory the basic variables are the elements of a compact Lie group, the present lattice model resembles the continuum theory in that the basic variables A are elements of the corresponding Lie algebra, a non-compact space. The lattice gauge invariance of Wilson's theory is lost. As in the continuum, the action is a quartic polynomial in A, and a stochastic gauge fixing mechanism - which is covariant in the continuum and avoids Faddeev-Popov ghosts and the Gribov ambiguity — is also transcribed to the lattice. It is shown that the model is self-compactifying, in the sense that the probability distribution is concentrated around a compact region of the hyperplane div A = 0 which is bounded by the Gribov horizon. The model is simulated numerically by a Monte Carlo method based on the random walk process. Measurements of Wilson loops, Polyakov loops and correlations of Polyakov loops are reported and analyzed. No evidence of confinement is found for the values of the parameters studied, even in the strong coupling regime.     

The string tension of compact U(1) four-dimensional lattice gauge theory

Monte Carlo simulations of the string tension are calculated for four-dimensional U(1) gauge theory on a 6⁴ lattice. The string tension follows the result -1n(β/2) in the high temperature region and is zero for β > β_c, where β_c is the critical inverse temperature.     

Charge polarization in compact lattice QED

We investigate the polarization cloud around static electric charges in the framework of compact lattice QED. We calculate the correlations of Polyakov loops with the electric charge densityψ ^? ψ normalized to the chiral condensate. It turns out that virtual anticharges screen static charges as expected from continuum QED. Charge polarization is more pronounced at strong couplings and extends to a longer range on the lattice in the weak coupling phase. In both phases the correlations decrease with larger fermion mass.     

Polyakov loop correlations in Landau gauge and the heavy quark potential

We calculate Polyakov loop correlation functions in SU(3) gauge theory on a 12³ × 4 lattice. We determine from this the colour average heavy quark potential and compare it with the corresponding colour singlet potential in Landau gauge. A comparison with finite temperature perturbation theory shows that perturbative relations are at best recovered for very high temperatures.     

Testing the rotational symmetry of theSU(3) potential

We test the static quark-antiquark potential inSU(3) lattice gauge theory, at β=5.8 on a 16⁴ lattice. We find an anisotropy on the level of 3% for small distances,r?3a. We discuss the implications of this effect on the determination of the string tension.     

Effects of mesonic correlations in the QCD phase transition

The finite-temperature phase transition of strongly interacting matter is studied within a nonlocal chiral quark model of the NJL type coupled to a Polyakov loop. In contrast to previous investigations which were restricted to the mean-field approximation, mesonic correlations are included by evaluating the quark-antiquark ring sum. For physical pion masses, we find that the pions dominate the pressure below the phase transition, whereas above T _c the pressure is well described by the mean-field-approximation result. For large pion masses, as realized in lattice simulations, the meson effects are suppressed. The text was submitted by the authors in English.     

Intermediate asymptotic expressions for high-order spin correlation functions in a two-dimensional classical ferromagnet

Different-point spin correlation functions are calculated for a two-dimensional classical ferromagnet in a pacerturbative range of distances r: a<r?m ^?1, where a is the lattice parameter and m ^?1 is the correlation length. The expressions for the four-and higher-order correlation functions are presented.     

Monte Carlo studies of wilson loops in four-dimensional U(2) gauge theory

Wilson loops are calculated using Monte Carlo simulations for pure U(2) gauge theory on a 6⁴ lattice. The loops appear to contain an area law piece in both the high and low temperature regions. The string tension is discontinuous at β = β_c, where β_c is the critical inverse temperature. This suggests that the first-order phase transition in U(2) gauge theory is not a deconfining phase transition. The determinant of the Wilson loop, however, extracts the U(1) part of the theory and appears to lose the area law at low temperature.     

Improved continuum limit lattice action for QCD with wilson fermions

Two possible ways of extending Symanzik's improvement programme to lattice fermions namely improvement to first and second order in the lattice sppacing a are discussed. The corresponding lattice actions for fermions are constructed and tree-level improvement conditions are derived by considering “classical” improvement. The concept of “on-shell” improvement is generalized to the lattice fermions studied here and the free parameters are determined for O(a) and O(a²) on-shell improved actions to all orders of perturbation theory. No evidence is found that the complicated structure of the O(a²) on-shell improved action, especially thearising fermion contact terms can be removed beyond tree level. The effect of terms in the action that explicitly break chiral symmetry and therefore remove the phenomenon of species doubling are investigated by considering the energy-momentum relations of the arising tree-level improved actions. Our main result is that the O(a) improved action is a slightly modified Wilson fermion action can still be written with only nearest-neighbour fermion interactions.     

SU(2) Lattice gauge theory in (2+1)D

Cluster expansion methods are applied to theSU(2) lattice gauge model in (2+1) dimensions. Strong-coupling series are calculated for the vacuum energy per site, the axial string tension, and the scalar mass gap; while ELCE approximants are used to estimate the string tension beyond its roughening transition. The simple scaling behaviour expected of this super-renormalizable theory is clearly seen, and we estimate that in the continuum limit the string tension σ～(0.14±0.01)g ⁴, while the mass gapM _s ～(2.2±0.25)g ². More accurate Monte Carlo simulations are needed to check the universality between the Hamiltonian and Euclidean versions of this model.     

Baryon terms in lattice gauge theories at finite temperature

We consider Susskind fermions on ad-dimensional lattice interacting withSU(n) gauge fields at finite temperature in the strong coupling limit. We demonstrate that the baryon terms can be treated perturbatively. Their effect on the Wilson loop parameter is calculated.     

Weak correction to the muon magnetic moment in a gauge model

The weak correction, a_μ^w, to the anomalous magnetic moment of the muon is calculated in an SU(2) ? U(1) ? U(1) gauge model of weak and electromagnetic interactions. The R_ξ gauge is used and Ward-Takahashi indentities are utilized eliminating all ξ-dependence before the loop integration is performed. a_μ^w,expt places no constraint on the mass of one of the neutral vector mesons, which may be arbitrarily small.     

Coercivity mechanism of Sm(Co, Cu)5

The mechanism of the high intrinsic coercivity of the Sm(Co_1−xCu_x)₅ (0≦x<1) system was studied by relating the coherency between the lattice constants of hexagonal Sm(Co, Cu)₅ and hcp Co to the coercive force. It was found analytically that the intrinsic coercive force reaches a maximum in the composition range from x=0.6 to 0.8, where the lattice mismatch approaches zero, so that there is a strong correlation between lattice matching and coercive force. When a Sm ion was located within a Sm(Co, Cu)₅ grain and in the outmost edge of the a and c planes of its grain surrounded or not surrounded by the coherent Co phase, the crystal field parameter at each Sm³⁺ site was calculated using a point charge model under the assumption that the Co and Cu atoms located in a grain and the hcp Co atoms situated at the interface uniformly have a charge of 3/5−. The results indicated that the Co phase precipitated coherently along the grain boundaries effectively enhances the magnetocrystalline anisotropy of Sm ions located in the outmost edges of the a and c planes of a Sm(Co, Cu)₅ grain.     

Volumenänderung durch Gitterverzerrung um ein F-Zentrum in Alkalihalogenidkristallen

The lattice-distortions in the vicinity of anF-centre in alkalihalide crystals and the volume change arising from the lattice distortions around this defect are being calculated. Only theF-centre ground state is considered and the effect of lattice vibrations is neglected. The interaction of theF-electron with the ions is described in terms of effective potentials, and a vacancy-centered wave function is calculated for theF-electron. In calculating the lattice distortions, an approximative procedure is adopted in which only the ions in the vicinity of anF-centre receive an atomistic treatment whereas the remainder of the crystal is treated as an elastic continuum. The volume change caused by the lattice distortions around anF-centre is calculated, using a method ofFischer andHahn which does not require an exact knowledge of the asymptotic strainfield around the point defect. The ions of the first, second and third shell around theF-centre-vacancy are found to be displaced in an outward direction. For the volume-change perF-centre the following values were obtained: 0.26a ³ in NaCl, 0.31a ³ in KCl and 0.35a ³ in KBr,a being the interionic distance. In order to check the validity of some of the approximations employed in the calculations, the volume changes caused by substitution of alien alkali- or halideions are computed and are found to be in good agreement with experimental data.     

Weak coupling perturbative calculations of the Wilson loop in lattice gauge theory

Weak coupling perturbative calculations of the Wilson loop in lattice gauge theory are carried out numerically up to order g⁴. Comparison of the results with those of the Monte Carlo calculations shows that there exists a non-perturbative contribution of an essential singularity type which may be identified as the string tension.     

Nonperturbative equation of state of quark-gluon plasma

The paper is devoted to the systematic derivation of nonperturbative thermodynamics of quark-gluon plasma, on the basis of the background perturbation theory. Vacuum background fields enter only in the form of field correlators, which are known from lattice and analytic calculations. In the lowest order in α_s the purely nonperturbative sQGP thermodynamics is expressed through single quark and gluon lines (single line approximation) which are interacting nonperturbatively with vacuum fields and with other lines. Nonperturbative EOS is obtained in terms (of the absolute value) of fundamental (adjoint) Polyakov loop L_fund(adj) and spatial string tension σ_s(T). In the lowest approximation the pressure for quarks (gluons) has a simple factorized form P_q(g) = P_SBL_fund(adj), where L_i describe the action of vacuum colorelectric fields on particle trajectory.