We introduce some modern mathematical and theoretical tools in 2-dimensional physics, and apply them to the Ising model. We rederive some well-known results, but also some new properties of this important model. All the tools presented here have applications for beyond the Ising model.
We explore several aspects of conformal field theory, proving, analysing, and testing Zamolodchikov's C-theorem. We explore finite size effects in critical and non-critical systems on the cylinder and the torus, and discuss the implications of modular invariance. Using BCFT, we explore the implications for theories with a boundary, and look at an interesting relationship between BCFTs and non-critical theories for integrable models, which indicates that there is a deep link between conformal symmetry and the symmetry of integrability. Finally we explore the holographic projection of critical and off-critical models which relates flat 2-dimensional models to 3-dimensional gravity.