We study, with various methods (standard large N evaluation of the functional integral for the effective potential, solution of the Schwinger-Dyson equations), the high temperature phase transition for the Ncomponent \phi^4theory in the large Nlimit. Our results fully confirm a previous investigation of the problem, for arbitrary N with the method of the average potential which employs renormalization group ideas. The phase transition is of the second order with an effectively three-dimensional critical behaviour. }

Abstract The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for viable ultraviolet completions in fundamental physics. It provides us with a natural framework to study theoretical models where degrees of freedom are correlated over long distances and that may exhibit very distinct behavior on different energy scales. ...

We study the thermodynamics of the relativistic quantum O(N ) model in two space dimensions. In the vicinity of the zero-temperature quantum critical point (QCP), the pressure can be written in the scaling form P (T ) = P (0) + N (T 3 /c 2 )FN (�/T ), where c is the velocity of the excitations at the QCP and |� | a characteristic zero-temperature energy scale. Using both a large-N approach to leading order and the nonperturbative renormalization group, we compute the universal scaling function F...

I give a brief overview of our present understanding of the high temperature phase of QCD, trying to clarify some of the theoretical issues involved in the current discussions that emphasize the strongly coupled character of the quark-gluon plasma produced at RHIC.

Abstract We use the non-perturbative renormalization group to clarify some features of perturbation theory in thermal field theory. For the specific case of the scalar field theory with O ( N ) symmetry, we solve the flow equations within the local potential approximation. This approximation reproduces the perturbative results for the screening mass and the pressure up to order g 3 , and starts to differ at order g 4 . The method allows a smooth extrapolation to the regime where the coupling is ...

#1Antal Jakovác(BME: Budapest University of Technology and Economics)H-Index: 14

#2András Patkós(ELTE: Eötvös Loránd University)H-Index: 15

Last. P. Szépfalusy(MTA: Hungarian Academy of Sciences)H-Index: 14

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Using a gap equation for the pion mass a non-perturbative method is given for solving the chiral quark-meson model in the chiral limit at the lowest order in the fermion contributions encountered in a large-N fapproximation. The location of the tricritical point is analytically determined. A mean field potential is constructed from which critical exponents can be obtained.

We present results from numerical studies of the finite temperature phase transition of the (3+1)d O(N)-symmetric non-linear sigma model for N = 1,2 and 3. We study the dependence of the width of the 3d critical region on N and we show that the broken phase scaling region is much wider for N = 2 and 3 than for N = 1. We also compare the widths of the critical region in the low T and high T phases of the O(2) model and we show that the scaling region in the broken phase is much wider than in the ...

Solutions of the Polchinski exact renormalization group equation in the scalar O(N) theory are studied. Families of regular solutions are found and their relation with fixed points of the theory is established. Special attention is devoted to the limit N = ∞, where many properties can be analyzed analytically.

We propose a simple explanation for the connection between chiral symmetry restoration and deconfinement in QCD at high temperature. In the Higgs description of the QCD vacuum both spontaneous chiral symmetry breaking and effective gluon masses are generated by the condensate of a color octet quark-antiquark pair. The transition to the high-temperature state proceeds by the melting of this condensate. Quarks and gluons become (approximately) massless at the same critical temperature. For instant...

Abstract We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative solutions follow from approximations to the general form of the coarse-grained free energy or effective average action. They interpolate between the microphysical laws and the complex macroscopic phenomena. Our approach yields a simple unified descriptio...

Using the Matsubara formalism, we consider the massive (λ4)D vector N-component model in the large-N limit, the system being confined between two infinite parallel planes. We investigate the behaviour of the coupling constant as a function of the separation L between the planes. For the Wick-ordered model in D = 3 we are able to give an exact formula to the L dependence of the coupling constant. For the non-Wick-ordered model we indicate how expressions for the coupling constant and the mass can...