Phase transitions and scaling limits in lattice models (Zhongyang Li - UConn)
- Starts: 4:00 pm on Thursday, December 6, 2018
- Ends: 5:00 pm on Thursday, December 6, 2018
Abstract: The perfect matching is a subset of a graph where each vertex is incident to exactly one edge. It is a natural mathematical model for molecule structures, and can provide exact solutions to various other statistical mechanical models, including the celebrated Ising model and the 1-2 model. We will discuss the limit shape of the perfect matching when a rescaled graph approximates a certain simply-connected domain in the plane, as well as the frozen boundary, which is the boundary separating the frozen region and the liquid region. A closely related model is the 1-2 model, which is a probability measure on subgraphs of the hexagonal lattice where each vertex is incident to 1 or 2 edges. With the help of the dimer model, we can obtain a sharp phase transition result for the 1-2 model. We will also discuss the exact formula to compute the probability that a path occurs in a 1-2 model configuration, and almost sure non-existence of an infinite path, with the help of the mass-transport principle.
- MCS 148, 111 Cummington Mall