How does a large system made of many small, interacting, randomly moving parts, behave? Nowadays, this kind of questions arises everywhere in natural and social sciences, but it is the most studied in the context of statistical mechanics, or thermodynamics, where the small parts might corresponds e.g. to atoms in the crystal lattice. In the eighties, physicists made a number of powerful conjectures connecting these questions, in the two-dimensional case, to quantum field theory and string theory. Assuming this connection to be true, they were able to compute many physically relevant quantities exactly. However, to date there is not a single lattice model for which these methods would be justified in full and rigorously. This project strives to bridge this gap, by verifying that several lattice models, in particular, the two-dimensional Ising model, indeed carries the deep field-theoretic structures as predicted in the physics literature.

2024

2028