Zeri di Lee-Yang per una teoria quantistica di campo

We study phase transition phenomena in a quantum field theory formalism. This is carried out using a technique based on Lee-Yang zeros, which was originally developed for statistical mechanics systems. We discuss various integrable quantum field theories (both in the relativistic and in the non-relativistic regime), and analyze different systems, including the Lieb-Liniger model, the Lee-Yang model and the Sinh-Gordon, working out the solution to their thermodynamic Bethe Ansatz equations to reconstruct their thermodynamics. We develop the mathematical tools for a numerical determination of Yang-Lee zeros and test them first in a toy model, then in the the Lee-Yang and Sinh-Gordon models.