Heating the O(N) nonlinear sigma model

The thermodynamics of the O(N) nonlinear sigma model in 1+1 dimensions is studied. We calculate the finite temperature effective potential in leading order in the 1/N expansion and show that at this order the effective potential can be made finite by temperature independent renormalization. We will show that this is not longer possible at next-to-leading order in 1/N. In that case one can only renormalize the minimum of the effective potential in a temperature independent way, which gives us finite physical quantities like the pressure.Comment: 8 pages, 2 figures, Seminar talk given at the 43st Cracow School of Theoretical Physics, 30 May - 8 June 2003, Zakopane, Polan

Thermodynamics of the O(N) Nonlinear Sigma Model in 1+1 Dimensions

The thermodynamics of the O(N) nonlinear sigma model in 1+1 dimensions is studied. We calculate the pressure to next-to-leading order in the 1/N expansion and show that at this order, only the minimum of the effective potential can be rendered finite by temperature-independent renormalization. To obtain a finite effective potential away from the minimum requires an arbitrary choice of prescription, which implies that the temperature dependence is ambiguous. We show that the problem is linked to thermal infrared renormalons.Comment: 8 pages, revtex, 3 eps figures; reference added, improved figure 1, minor other changes, conclusions unchange

Color superconductivity vs. pseudoscalar condensation in a three-flavor NJL model

We calculate numerically the phase diagram of the three-flavor Nambu-Jona-Lasinio model at zero and finite temperature as a function of the up, down, and strange quark chemical potentials. We focus on the competition between pseudoscalar condensation and color superconductivity. We find that the two types of phases are separated by first-order transitions.Comment: 8 pages, 7 figures, revtex. References added, minor other changes, conclusions unchanged. To appear in PR

The effects of quantum instantons on the thermodynamics of the CP^(N-1) model

Using the 1/N expansion, we study the influence of quantum instantons on the thermodynamics of the CP^(N-1) model in 1+1 dimensions. We do this by calculating the pressure to next-to-leading order in 1/N, without quantum instanton contributions. The fact that the CP^1 model is equivalent to the O(3) nonlinear sigma model, allows for a comparison to the full pressure up to 1/N^2 corrections for N=3. Assuming validity of the 1/N expansion for the CP^1 model makes it possible to argue that the pressure for intermediate temperatures is dominated by the effects of quantum instantons. A similar conclusion can be drawn for general N values by using the fact that the entropy should always be positive.Comment: 7 pages, 5 figures, revtex. To appear in PRD. Some arguments and conclusions reformulate

Color superconducting matter in a magnetic field

We investigate the effect of a magnetic field on cold dense three-flavor quark matter using an effective model with four-Fermi interactions with electric and color neutrality taken into account. The gap parameters Delta_1, Delta_2, and Delta_3 representing respectively the predominant pairing between down and strange (d-s) quarks, strange and up (s-u) quarks, and up and down (u-d) quarks, show the de Haas-van Alphen effect, i.e. oscillatory behavior as a function of the modified magnetic field B that can penetrate the color superconducting medium. Without applying electric and color neutrality we find Delta_2 \approx Delta_3 >> Delta_1 for 2 e B / mu_q^2, where e is the modified electromagnetic coupling constant and mu_q is one third of the baryon chemical potential. Because the average Fermi surface for each pairing is affected by taking into account neutrality, the gap structure changes drastically in this case; we find Delta_1 >> Delta_2 \approx Delta_3 for 2 e B > mu_q^2. We point out that the magnetic fields as strong as presumably existing inside magnetars might induce significant deviations from the gap structure Delta_1 \approx Delta_2 \approx Delta_3 at zero magnetic field.Comment: 5 pages, 3 figure

Thermodynamics of QCD-inspired theories

In this thesis I investigate the thermodynamics of the O(N) nonlinear sigma model and the CP^(N-1) model in 1 + 1 dimensions, which are toy models for QCD. In particular I put emphasis on the calculation of the effective potential and the pressure to next-to-leading order in 1/N. One interesting result is that the effective potential contains temperature-dependent ultraviolet divergences that vanish in the minimum. Furthermore I discuss two low-energy effective theories, the O(N) linear sigma model in 3 + 1 dimensions and the NJL model. In the O(N) model I calculate the effective potential and the pressure up to next-to-leading order in 1/N. I also discuss a rather low bound on the mass of the sigma meson in that model. The NJL model is used to calculate phase diagrams with pseudoscalar condensation and color superconductivity as a function of different quark chemical potentials. I find that phases with pseudoscalar condensation are separated from the color superconducting phases by a first order transtion.Comment: 171 pages, Ph.D. thesis, printed booklet available upon reques