Given a graph G with vertex set V and edge set E, a spin system is a probability distribution on the graph that assigns a value of +1 (an up spin) or -1 (a down spin) to each of the graph's vertices. The physical interpretation is that magnets, each having one of the two possible orientations (represented by +1 and −1) are placed on the vertices of the graph; accordingly, the graph will have an associated free energy depending on the orientations of these magnets. The nearest-neighbor Ising model is one of the most widely studied spin systems, where Glauber dynamics describe how the system's free energy evolves over time.
This project considers Glauber dynamics for the Gibbs probability measure on a random regular hypergraph. In particular, it investigates the mixing time of Glauber dynamics computationally and how the mixing time changes depending on a certain temperature parameter.