Method for comparing finite temperature field theory results with lattice data

The values of the presently available truncated perturbative expressions for the pressure of the quark-gluon plasma at finite temperatures and finite chemical potential are trustworthy only at very large energies. When used down to temperatures close to the critical one Tc, they suffer from large uncertainties due to the renormalization scale freedom. In order to reduce these uncertainties, we perform resummations of the pressure by applying Pade-related approximants to the available perturbation series for the short-distance and for the long-distance contributions. In the two contributions, we use two different renormalization scales which reflect different energy regions contributing to the different parts. Application of the obtained expressions at low temperatures is made possible by replacing the usual four-loop barMS beta function for alpha_s by its Borel-Pade resummation, eliminating thus the unphysical Landau singularities of alpha_s. The obtained results are remarkably insensitive to the chosen renormalization scale and can be compared with lattice results -- for the pressure (p), the chemical potential contribution (delta p) to the pressure, and various susceptibilities. A good qualitative agreement with the lattice results is revealed down to temperatures close to Tc.Comment: 24 pages, 17 figures, revtex4; Ref.[25] is new; the ordering of the references and grammatic and stylistic errors are corrected - version as it appears in PR

Scaling behavior at zero-temperature critical points

A scaling form for the logarithm of the partition function suitable for a zero-temperature critical point is obtained and found to hold for the spherical model in less than two dimensions and the classical n-component Heisenberg linear chain. Nevertheless, several cases are found where the critical-exponent relations involving the specific heat fail. These anomalous cases do not imply a breakdown of the scaling implicit in the basic formulation of renormalization-group theory

Critical indices from perturbation analysis of the Callan-Symanzik equation

Recent results giving both the asymptotic behavior and the explicit values of the leading-order perturbation-expansion terms in fixed dimension for the coefficients of the Callan-Symanzik equation are analyzed by the the Borel-Leroy, Padé-approximant method for the n-component φ^4 model. Estimates of the critical exponents for these models are obtained for n=0, 1, 2, and 3 in three dimensions with a typical accuracy of a few one thousandths. In two dimensions less accurate results are obtained

Improved Quantum Hard-Sphere Ground-State Equations of State

The London ground-state energy formula as a function of number density for a system of identical boson hard spheres, corrected for the reduced mass of a pair of particles in a sphere-of-influence picture, and generalized to fermion hard-sphere systems with two and four intrinsic degrees of freedom, has a double-pole at the ultimate \textit{regular} (or periodic, e.g., face-centered-cubic) close-packing density usually associated with a crystalline branch. Improved fluid branches are contructed based upon exact, field-theoretic perturbation-theory low-density expansions for many-boson and many-fermion systems, appropriately extrapolated to intermediate densities, but whose ultimate density is irregular or \textit{random} closest close-packing as suggested in studies of a classical system of hard spheres. Results show substantially improved agreement with the best available Green-function Monte Carlo and diffusion Monte Carlo simulations for bosons, as well as with ladder, variational Fermi hypernetted chain, and so-called L-expansion data for two-component fermions.Comment: 15 pages and 7 figure

Pade-related resummations of the pressure of quark-gluon plasma by approximate inclusion of g**6-terms

We perform various resummations of the hot QCD pressure based on the actual knowledge of the perturbation series which includes the g**6 ln(1/g) and part of the g**6 terms. Resummations are performed separately for the short- and long-distance parts. The g**6 term of the short-distance pressure is estimated on the basis on the known UV cutoff dependence of the long-distance part. The resummations are of the Pade and Borel-Pade type, using in addition the (Pade-)resummed expression for the squared screening mass mE**2 and for the EQCD coupling parameter gE**2. The resummed results depend weakly on the yet unknown g**6 terms and on the the short-range renormalization scale, at all temperatures. The dependence on the long-range renormalization scale is appreciable at low temperatures T < 1 GeV. The resulting dependence of pressure on temperature T is compatible with the results of the lattice calculations at low T.Comment: 25 pages, 15 double figures, 4 single figures, revtex4; thoroughly extended analysis; more figures; conclusions more clearly formulated; new references added; title slightly changed; accepted for publication in Phys.Rev.

Ising-Model Critical Indices in Three Dimensions from the Callan-Symanzik Equation

The coefficients in the Callan-Symanzik equations for a three-dimensional, continuous spin Ising model with an exp(-As^4+Bs^2) spin-weight factor are expanded in the dimensionless, renormalized coupling constant. These series are summed by the Padé-Borel method to yield the critical indices γ=1.241±0.002, η=0.02±0.02, ν=0.63±0.01, and Δ1=0.49±0.01

Applying generalized Pad\'e approximants in analytic QCD models

A method of resummation of truncated perturbation series, related to diagonal Pad\'e approximants but giving results independent of the renormalization scale, was developed more than ten years ago by us with a view of applying it in perturbative QCD. We now apply this method in analytic QCD models, i.e., models where the running coupling has no unphysical singularities, and we show that the method has attractive features such as a rapid convergence. The method can be regarded as a generalization of the scale-setting methods of Stevenson, Grunberg, and Brodsky-Lepage-Mackenzie. The method involves the fixing of various scales and weight coefficients via an auxiliary construction of diagonal Pad\'e approximant. In low-energy QCD observables, some of these scales become sometimes low at high order, which prevents the method from being effective in perturbative QCD where the coupling has unphysical singularities at low spacelike momenta. There are no such problems in analytic QCD.Comment: 14 pages; extended presentation of the analytic QCD models in Sec.IV; two references added ([37,38]); version to appear in Phys.Rev.