The file is restricted for YU community access only.
In this thesis, I study the static properties and dynamics of a quantum system of
interacting particles. For this, I employ the laws of quantum mechanics, which differ from
the laws of classical mechanics used to interpret the macroscopic world around us. Quantum
mechanics is a branch of physics that describes how matter and light behave on a
microscopic level. My focus is on a lattice system that has on each site a localized particle
with spin ½. Spins are intrinsic properties of microscopic particles that tell us how they react
to magnetic fields. The basic constituents of matter, such as electrons, protons, and neutrons,
have spins ½, while atoms have higher values of spins. The interactions between the spins
may lead to collective behaviors with macroscopic effects, such as ferromagnetism, where
the spins line up parallel to each other, and antiferromagnetism, where neighboring spins
point in opposite directions.