Phase transitions in quantum field theory

Abstract

In this thesis we deal with aspects related to phase transitions in quantum field theories. We focus in aspects of thermal field theory: QCD at high temperature under the influence of strong magnetic fields and a novel application of a method from statistical mechanics to field theories.

In the first part of the work we studied two-color QCD in a constant external magnetic background at finite temperature using the Polyakov-loop extended two-flavor two-color Nambu-Jona-Lasinio model. Systems that can be described by such a model arise in various contexts. For example, magnetars, which are a certain type of neutron stars, have very strong magnetic fields. Some of the properties of stars such as the mass-radius relation are determined by the equation of state. The determination of the bulk properties of a Fermi gas in an external magnetic field is therefore important for the understanding of these compact stellar objects.

In the second part of our research, we promoted the applicability of the mean spherical approximation, a closure relation for pair correlation functions (two-point functions) in statistical physics, to euclidean quantum field theories formulated on a lattice. We demonstrated how the MSA can be used to locate the critical lines of a class of multi-component bosonic models. The MSA has the potential to handle models lacking a positive definite integration measure, which therefore are difficult to investigate by Monte-Carlo simulations.