Critical Phenomena in the Phase Diagrams of QCD-like Theories

QCD is the well-established theory of strong interactions but of such a complex nature that outstanding open questions remain even after almost 40 years since its discovery. In this thesis we concentrate on aspects of finite density QCD and the deconfinement transition, which we study, however, not in QCD itself but in QCD-like theories that are obtained by deformations of the QCD Lagrangian. In particular, we study effective models for 2-color QCD, adjoint QCD and QCD with isospin chemical potential as the three prototypical examples for QCD-like theories without a fermion sign problem and investigate their corresponding phase diagrams. One main tool in our analysis is the Functional Renormalization Group, which allows to consistently include quantum and thermal fluctuations and to study critical phenomena. A particular focus lies on two-color QCD, which provides a transparent demonstration of the impact of baryonic degrees of freedom: without them its phase diagram resembles that of corresponding 3-color model calculations including a critical endpoint which vanishes, however, inside the diquark condensation phase once one properly includes the diquarks as lightest baryonic degrees of freedom. Interesting relations to effective models for the BEC-BCS crossover in (non-relativistic) ultracold atomic gases arise, which are most transparently demonstrated in the comparison between QCD with isospin chemical potential and imbalanced Fermi gases. In the second part we study the deconfinement transition in 2+1 dimensional pure SU(N) lattice gauge theories using universality methods