Many-body systems with long-range power-law decaying potentials among their microscopic components are known to fall outside the traditional framework of complex systems. While some peculiarities in their behavior had emerged since the
very early days of statistical mechanics, the possibility of engineering such systems
in experimental setups based on molecular and optical systems has stimulated an im-
pressive theoretical activity in the last decades, unveiling a plethora of new physical
phenomena. In particular, depending on the exact form of the couplings, long-range-
interacting systems may avoid thermalization, remaining trapped in long-lived metastable phases, or exhibit new equilibrium phases at thermal equilibrium. The study of such novel phases, emerging both in the equilibrium behavior and in the dynamics, is the subject of the present thesis. In particular, in Part I the equilibrium behavior of long-range XY model and long-range Villain model are studied, while in the second part the quantum dynamics of long-range spin chains, both isolated and subjected to periodic driving, is investigated.
