Systems composed of many interacting parts often exhibit dramatically different properties from their components:

"There's no love in a carbon atom, no hurricane in a water molecule, [and] no financial collapse in a dollar bill."

I study how complex, emergent phenomena arise from simple microscopic rules within the framework of equilibrium statistical mechanics. Specifically, I use probabilistic and combinatorial methods to rigorously characterize the Gibbs measures of various idealized physical systems across different temperatures, densities, and other parameters.