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We study the Fourier coefficients b(k,T) of the net baryon number density in strongly interacting matter at finite temperature. We show that singularities in the complex chemical potential plane connected with phase transitions are reflected in the asymptotic behavior of the coefficients at large k. We derive the scaling properties of b(k,T) near a second order phase transition in the O(4) and Z(2) universality classes. The impact of first order and crossover transitions is also examined. The scaling properties of b(k,T) are linked to the QCD phase diagram in the temperature and complex chemical potential plane., Comment: 8 pages, 2 figures

We investigate the Fourier coefficients $b_k(T)$ of the net--baryon number density in strongly interacting matter at nonzero temperature and density. The asymptotic behavior of the coefficients at large $k$ is determined by the singularities of the partition function in the complex chemical potential plane. Within a QCD-like effective chiral model, we show that the chiral and deconfinement properties at nonzero baryon chemical potential are reflected in characteristic $k$-- and $T$-- dependences of the Fourier coefficients. We also discuss the influence of the Roberge-Weiss transition on these coefficients. Our results indicate that the Fourier expansion approach can provide interesting insights into the criticality of QCD matter., Comment: 16 pages, 18 figures, text updated, published in Phys. Rev. D

In this thesis we consider effective models of quantum chromodynamics to learn about the chiral- and deconfinement phase transitions. In Chapter 1 we review basic properties of strongly interacting matter and the foundations of finite temperature field theory. We review furthermore the nonperturbative functional renormalization group (FRG) approach. In Chapter 2 we introduce the quark-meson (QM) model and its extensions including the Polyakov-loop variables and repulsive vector interactions between quarks. We then discuss features of the model both in the mean-field approximation and in the renormalization group treatment. A novel method to solve the renormalization group equations based on the Chebyshev polynomials is presented at the end of the chapter. In Chapter 3 the scaling behavior of the order parameter at the chiral phase transition is studied within effective models. We explore universal and nonuniversal structures near the critical point. These include the scaling functions, the leading corrections to scaling and the corresponding size of the scaling window as well as their dependence on an external symmetry breaking field. We consider two models in the mean-field approximation, the QM and the Polyakov-loop-extended quark-meson (PQM) models, and compare their critical properties with a purely bosonic theory, the O(N) linear sigma model in the N → ∞ limit. In these models the order parameter scaling function is found analytically using the high temperature expansion of the thermodynamic potential. The effects of a gluonic background on the nonuniversal scaling parameters are studied within the PQM model. Furthermore, numerical calculations of the scaling function and the scaling window are performed in the QM model using the FRG. Chapter 4 contains a study of the critical properties of net-baryon-number fluctuations at the chiral restoration transition in a medium at finite temperature and net baryon density. The chiral dynamics of quantum chromodynamics i

In this thesis we consider effective models of quantum chromodynamics to learn about the chiral- and deconfinement phase transitions. In Chapter 1 we review basic properties of strongly interacting matter and the foundations of finite temperature field theory. We review furthermore the nonperturbative functional renormalization group (FRG) approach. In Chapter 2 we introduce the quark-meson (QM) model and its extensions including the Polyakov-loop variables and repulsive vector interactions between quarks. We then discuss features of the model both in the mean-field approximation and in the renormalization group treatment. A novel method to solve the renormalization group equations based on the Chebyshev polynomials is presented at the end of the chapter. In Chapter 3 the scaling behavior of the order parameter at the chiral phase transition is studied within effective models. We explore universal and nonuniversal structures near the critical point. These include the scaling functions, the leading corrections to scaling and the corresponding size of the scaling window as well as their dependence on an external symmetry breaking field. We consider two models in the mean-field approximation, the QM and the Polyakov-loop-extended quark-meson (PQM) models, and compare their critical properties with a purely bosonic theory, the O(N) linear sigma model in the N → ∞ limit. In these models the order parameter scaling function is found analytically using the high temperature expansion of the thermodynamic potential. The effects of a gluonic background on the nonuniversal scaling parameters are studied within the PQM model. Furthermore, numerical calculations of the scaling function and the scaling window are performed in the QM model using the FRG. Chapter 4 contains a study of the critical properties of net-baryon-number fluctuations at the chiral restoration transition in a medium at finite temperature and net baryon density. The chiral dynamics of quantum chromodynamics i

In this thesis we consider effective models of quantum chromodynamics to learn about the chiral- and deconfinement phase transitions. In Chapter 1 we review basic properties of strongly interacting matter and the foundations of finite temperature field theory. We review furthermore the nonperturbative functional renormalization group (FRG) approach. In Chapter 2 we introduce the quark-meson (QM) model and its extensions including the Polyakov-loop variables and repulsive vector interactions between quarks. We then discuss features of the model both in the mean-field approximation and in the renormalization group treatment. A novel method to solve the renormalization group equations based on the Chebyshev polynomials is presented at the end of the chapter. In Chapter 3 the scaling behavior of the order parameter at the chiral phase transition is studied within effective models. We explore universal and nonuniversal structures near the critical point. These include the scaling functions, the leading corrections to scaling and the corresponding size of the scaling window as well as their dependence on an external symmetry breaking field. We consider two models in the mean-field approximation, the QM and the Polyakov-loop-extended quark-meson (PQM) models, and compare their critical properties with a purely bosonic theory, the O(N) linear sigma model in the N → ∞ limit. In these models the order parameter scaling function is found analytically using the high temperature expansion of the thermodynamic potential. The effects of a gluonic background on the nonuniversal scaling parameters are studied within the PQM model. Furthermore, numerical calculations of the scaling function and the scaling window are performed in the QM model using the FRG. Chapter 4 contains a study of the critical properties of net-baryon-number fluctuations at the chiral restoration transition in a medium at finite temperature and net baryon density. The chiral dynamics of quantum chromodynamics i

In this thesis we consider effective models of quantum chromodynamics to learn about the chiral- and deconfinement phase transitions. In Chapter 1 we review basic properties of strongly interacting matter and the foundations of finite temperature field theory. We review furthermore the nonperturbative functional renormalization group (FRG) approach. In Chapter 2 we introduce the quark-meson (QM) model and its extensions including the Polyakov-loop variables and repulsive vector interactions between quarks. We then discuss features of the model both in the mean-field approximation and in the renormalization group treatment. A novel method to solve the renormalization group equations based on the Chebyshev polynomials is presented at the end of the chapter. In Chapter 3 the scaling behavior of the order parameter at the chiral phase transition is studied within effective models. We explore universal and nonuniversal structures near the critical point. These include the scaling functions, the leading corrections to scaling and the corresponding size of the scaling window as well as their dependence on an external symmetry breaking field. We consider two models in the mean-field approximation, the QM and the Polyakov-loop-extended quark-meson (PQM) models, and compare their critical properties with a purely bosonic theory, the O(N) linear sigma model in the N → ∞ limit. In these models the order parameter scaling function is found analytically using the high temperature expansion of the thermodynamic potential. The effects of a gluonic background on the nonuniversal scaling parameters are studied within the PQM model. Furthermore, numerical calculations of the scaling function and the scaling window are performed in the QM model using the FRG. Chapter 4 contains a study of the critical properties of net-baryon-number fluctuations at the chiral restoration transition in a medium at finite temperature and net baryon density. The chiral dynamics of quantum chromodynamics i

In this thesis we consider effective models of quantum chromodynamics to learn about the chiral- and deconfinement phase transitions. In Chapter 1 we review basic properties of strongly interacting matter and the foundations of finite temperature field theory. We review furthermore the nonperturbative functional renormalization group (FRG) approach. In Chapter 2 we introduce the quark-meson (QM) model and its extensions including the Polyakov-loop variables and repulsive vector interactions between quarks. We then discuss features of the model both in the mean-field approximation and in the renormalization group treatment. A novel method to solve the renormalization group equations based on the Chebyshev polynomials is presented at the end of the chapter. In Chapter 3 the scaling behavior of the order parameter at the chiral phase transition is studied within effective models. We explore universal and nonuniversal structures near the critical point. These include the scaling functions, the leading corrections to scaling and the corresponding size of the scaling window as well as their dependence on an external symmetry breaking field. We consider two models in the mean-field approximation, the QM and the Polyakov-loop-extended quark-meson (PQM) models, and compare their critical properties with a purely bosonic theory, the O(N) linear sigma model in the N → ∞ limit. In these models the order parameter scaling function is found analytically using the high temperature expansion of the thermodynamic potential. The effects of a gluonic background on the nonuniversal scaling parameters are studied within the PQM model. Furthermore, numerical calculations of the scaling function and the scaling window are performed in the QM model using the FRG. Chapter 4 contains a study of the critical properties of net-baryon-number fluctuations at the chiral restoration transition in a medium at finite temperature and net baryon density. The chiral dynamics of quantum chromodynamics i

The scaling behavior of the order parameter at the chiral phase transition, the so-called magnetic equation of state, of strongly interacting matter is studied within effective models. We explore universal and nonuniversal structures near the critical point. These include the scaling functions, the leading corrections to scaling, and the corresponding size of the scaling window as well as their dependence on an external symmetry breaking field. We consider two models in the mean-field approximation, the quark-meson and the Polyakov loop extended quark-meson (PQM) models, and compare their critical properties with a purely bosonic theory, the $O(N)$ linear sigma model in the $N\rightarrow \infty$ limit. In these models the order parameter scaling function is found analytically using the high temperature expansion of the thermodynamic potential. The effects of a gluonic background on the nonuniversal scaling parameters are studied within the PQM model., Comment: 14 pages, 8 figures. Extended discussion of the results, slightly changed parameters in calculation for transparency. Additional correction of minor errors and change of format