Finite-size effects in high dimensional physical systems

Statistical mechanics is a branch of mathematical physics which seeks to explain how macroscopic behaviour can emerge from the interactions between a large number of microscopic particles. One of the main aims in this field is to understand how phenomena such as phase transitions emerge in large but finite systems of interacting particles. In this thesis, we clarify a number of open questions in a long-standing debate regarding the surprising role of boundary effects in high-dimensional systems of critical phenomena.