Trasformazione di dualità per la teoria di campo scalare su reticolo

In physics, a duality is an exact analytical reformulation of a model in terms of an equivalent description, based on different degrees of freedom. Dualities play a very important role in many areas of theoretical physics, ranging from classical electromagnetism to spin systems, to string theory. Often, dual formulations of the same physical model highlight its various properties, enable one to study it in complementary regimes, and reveal information on its phase structure and critical points. In this thesis project, a scalar field theory with quartic interactions is regularized on a Euclidean lattice, and reformulated in terms of dual variables; its physical properties are then studied non-perturbatively, by means of numerical Monte Carlo calculations.