Constructive fun with doodles: from diagram algebras to exact solutions
An informal introduction to loop models is presented. These models have become fundamental tools in the description of physical systems with nonlocal degrees of freedom such as polymers and percolation. Their basic degrees of freedom are encoded in connectivities and are thus topological in nature. As intimidating as this may sound, underlying diagram algebras offer unlimited doodling fun for the whole family and can be used to establish integrability of the associated physical models. Critical dense polymers, in particular, can subsequently be solved exactly in a way rivalled only by the Ising model.