Interplay between local and global symmetries in critical lattice systems with matter fields

This thesis examines critical phenomena within statistical lattice systems, emphasizing the interplay of non-abelian local and global invariances in scalar field theories close to a critical phenomenon. These studies include numerical simulations in two- and three-dimensional lattice systems, encompassing different gauge representations and lattice Hamiltonians. We have used Monte Carlo simulations and Finite-Size Scaling theory to study the non-perturbative properties of the theories addressed.