# Student Probability Seminar

#### Low temperature Ising models and interfaces

**Speaker:**
Reza Gheissari, CIMS

**Location:**
Warren Weaver Hall 512

**Date:**
Wednesday, November 28, 2018, noon

**Synopsis:**

The Ising model is one of the most studied models of statistical physics. On the physically relevant 2D and 3D lattices, it has a famous phase transition between a disordered high-temperature phase (T>T_c) and a low-temperature phase (T<T_c) where a long-range order emerges. We study properties of this low temperature phase, first proving its existence via a classical Peierls argument. We then discuss a tool known as cluster expansion as a technique to view the low temperature phase as a perturbation of the model at zero temperature. We use this to analyze interfaces between the plus and minus phases of the Ising model at low-temperature: in 2D these interfaces undergo normal fluctuations (diverging in the system size) while in 3D they are rigid (with tight fluctuations).