Renormalization Group Approach to Hot and Dense Matter.
Technische Universität, Darmstadt
[Ph.D. Thesis], (2009)
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|Item Type:||Ph.D. Thesis|
|Title:||Renormalization Group Approach to Hot and Dense Matter|
The chiral quark-meson model, being an effective low-energy realization for spontaneous chiral symmetry breaking of QCD at intermediate momentum scales, is often used to study various properties of strongly interacting matter. In this thesis we employ this model to investigate the critical behavior of hot and dense matter with two degenerate light flavors. Using the method of the functional renormalization group, we derive the flow equation for the scale dependent thermodynamic potential at finite temperature and chemical potential in the presence of an explicit symmetry breaking term. We explore the scaling behavior of various observables and confront our results with the Widom-Griffiths form of the equation of state. The focus of our study are especially the scaling properties of the order parameter and its transverse and longitudinal susceptibilities for small, but finite values of the external field when approaching the critical point from the symmetric as well as from the broken phase. We also explore the thermodynamics and the phase structure of strongly interacting hot and dense matter. Apart from the renormalization group formalism, here we also employ the mean field approximation in order to investigate thermodynamic observables sensitive to the phase transition. As an effective model, we use the Polyakov loop extended two flavor chiral quark-meson model in order to connect the chiral and confining properties of QCD. The gluon dynamics is included by coupling quarks with the Polyakov loop and by introducing an effective Polyakov loop potential. We discuss the properties of the net quark number fluctuations in the vicinity of the QCD chiral phase transition. Our main focus of exploration is the ratio of the fourth- to second- order cumulants (kurtosis) and the compressibility. The sensitivity of both observables to the values of the pion mass near the chiral phase transition is also discussed. Within the renormalization group approach, the thermodynamics and the phase structure of the Polyakov loop extended quark-meson model is the main focus of our study. We propose an extended truncation of the effective average action with quarks coupled to background gluonic fields and derive the corresponding flow equation for the scale dependent thermodynamic potential. A full RG treatment of all fields is very complex and thus while solving the flow equation for the quark and meson fields we use the mean field results obtained previously for the Polyakov loop and its conjugate. Thus, within this scheme we determine the phase structure of the model and employ the Taylor expansion coefficients of the thermodynamic pressure in order to locate the position of the critical end point in the phase diagram. Due to the inclusion of fluctuations, we observe a change of the phase diagram compared to that obtained in the mean field approximation. In the end we also briefly discuss the cutoff effect present in the renormalization group method.
|Place of Publication:||Darmstadt|
|Uncontrolled Keywords:||Renormalization group, thermal field theory, critical phenomena|
|Classification DDC:||500 Naturwissenschaften und Mathematik > 530 Physik|
|Divisions:||05 Department of Physics|
|Date Deposited:||19 Jan 2009 07:35|
|Last Modified:||07 Dec 2012 11:54|
|Referees:||Friman, Prof. Dr. Bengt and Wambach, Prof. Dr. Jochen|
|Refereed:||22 December 2008|