ETD

• Abelian Higgs models
• finite-size scaling
• lattice gauge theory
• phase transitions

Three-dimensional Abelian Higgs theories are used to describe numerous emergent phenomena in condensed-matter physics, e.g. superconductivity, as well as to investigate fundamental theoretical aspects of the Higgs mechanism at a non-perturbative level. In both low and high-energy physics, non-perturbative properties can be inferred from the critical behaviour of lattice discretisations of Abelian Higgs models, in either three or four dimensions. The advances in numerical methods have enabled a more detailed characterisation and classification of the critical behaviours occurring in Abelian Higgs lattice models with different lattice formulations.
This thesis aims to classify the phase transition between the disordered-confined and the ordered-deconfined phases of the charged multicomponent lattice Abelian Higgs model discretised with compact gauge fields. This model shows both U$(1)$ gauge invariance and SU$(N)$ global symmetry associated with charged $N$-component scalar fields.
In particular, we focus on the analysis of specific values of the number of matter components, assessing the nature of the phase transitions via Monte-Carlo numerical simulations and consequent FSS analyses.