Temperature Dependence of the QCD Coupling

We present a one-loop calculation of a gauge invariant QCD beta function. Using both momentum and temperature renormalization group equations we investigate the running coupling in the magnetic sector as a function of temperature and momentum scale. At fixed momentum scale we find that, in contrast to $\lambda\phi^4$ or QED, high-temperature QCD is strongly coupled, even after renormalization group improvement. However, if the momentum scale is changed simultaneously with temperature in a specified manner, the coupling decreases. We also point out in what regime dimensional reduction occurs. Both the cases $N_f$ smaller and larger than $\frac{11}{2} N_c$ are discussed.Comment: 10 pages, LaTeX (5 postscript figures available), ITFA-93-11,THU-93/0

Critical Temperature and Amplitude Ratios from a Finite-Temperature Renormalization Group

We study \l\f^4 theory using an environmentally friendly finite-temperature renormalization group. We derive flow equations, using a fiducial temperature as flow parameter, develop them perturbatively in an expansion free from ultraviolet and infrared divergences, then integrate them numerically from zero to temperatures above the critical temperature. The critical temperature, at which the mass vanishes, is obtained by integrating the flow equations and is determined as a function of the zero-temperature mass and coupling. We calculate the field expectation value and minimum of the effective potential as functions of temperature and derive some universal amplitude ratios which connect the broken and symmetric phases of the theory. The latter are found to be in good agreement with those of the three-dimensional Ising model obtained from high- and low-temperature series expansions.Comment: 14 pages of LaTeX. Postscript figures available upon request form [email protected]

The Finite-Temperature Renormalization Group Applied to λϕ⁴ Theory and QCD

In this paper we apply the finite-temperature renormalization group from the point of view of “environmentally friendly” renormalization. We study both λϕ⁴ theory and the magnetic sector of QCD. At one loop level the complete temperature range of λϕ⁴ is successfully described in terms of the parameters of the zero temperature theory. We show also how the critical temperature can be calculated in terms of the latter. For the magnetic sector of QCD, in distinction to λϕ⁴, a one-loop finite temperature renormalization group improvement is not sufficient to describe the high-temperature regime