Aspects of phase transitions in gauge theories and spin models on the lattice

Abstract

The main focus of this thesis are phase transitions both in gauge theories, in particular in Quantum ChromoDynamics (QCD), and in two-dimensional spin models. The approach is numeric, relying on dedicated simulation and analysis softwares, and takes advantage of the possibility to discretize our theories, and describe our models, on a lattice. Three di erent kind of investigations have been carried out, two of them concerning QCD. The thermal decon nement/chiral phase transition in QCD at zero chemical potential has been indeed, indirectly studied, respectively via the characterization of color- eld ux tubes, as footprints for con nement in SU(3) pure gauge theory, and via a study at imaginary chemical potential for the case of full QCD with two degenerate

avors of dynamical quarks Nf = 2. In the former case a systematic study of the longitudinal pro le of the chromoelectric eld produced by the strong interaction of a pair of quark and antiquark in the QCD vacuum has been realized, both at zero and nonzero temperature. Measurements have been performed in numerical simulations implementing the appropriate eld-related lattice operator. The characteristic sizes of the ux tubes have been extracted through a tting procedure based on a well known picture for the con nement phenomenon called \dual superconductor model" that traces an analogy between color con nement and superconductivity. Such a picture is found to successfully describe our numerical results for the chromoelectric eld distribution at zero temperature. Taking one step further in the dual analogy, the pro le of the ux tube has been then studied at nite temperature and across the decon nement transition. However, results indicate that the analogy cannot be pushed so far: as the temperature is increased towards and above the decon nement temperature Tc, the amplitude of the eld inside the ux tube gets considerably smaller, while the shape of the ux tube does not vary appreciably at the onset of decon nement. An "evaporation" of ux tubes is observed that has no counterpart in ordinary (type-II) superconductivity and let the tube structure survive the phase transition, consistently with observations in heavy-ion collision experiments. A somewhat di erent analysis about the thermal phase transition in Nf = 2 QCD (where direct studies are prevented either by the well known sign problem or by high numerical costs) can be carried out at imaginary values of chemical potential that are critical for the Roberge-Weiss (RW) phase transition. In particular, the nature of the RW phase transition at the endpoint of the rst order critical RW line has been investigated. It is found to depend on the quark masses in a way that it is a triple rst-order point in the limit of zero (in nite) masses and a second order critical endpoint at intermediate masses. Similar results are relevant for the understanding of the nature of the thermal transition at = 0. Coming to spin models and, to be more speci c, to two-dimensional spin models characterized by non-Abelian symmetry groups U(2) and SU(N) for N = 5; 8, the existence of in nite order (BKT) phase transition has been checked. Such transitions were expected on the basis of analytical computations and have been, indeed, numerically detected in all considered models. By means of nite size scaling analysis it has been also observed that the BKT phase transition that takes place in U(2) models belongs to the universality class of the two-dimensional XY model.