Student Probability Seminar

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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).