Lecture 1. Wednesday August 20, 14:00-17:00, Feynman Lecture Hall at ICTS
Venue: Feynman Lecture Hall
Class Timings: Wednesdays from 2:00 PM - 5:00 PM
Description:
Planar statistical physics models exhibit a wide range of beautiful phenomena. The study of two-dimensional percolation models has been at the forefront of many exciting developments in probability theory in the past few decades. In this course, we will study Fortuin-Kastelyn (FK) percolation models, which are a family of percolation models parametrized by $q\geq 0$. The case $q=1$ corresponds to Bernoulli bond percolation. These models are also intimately connected with Ising and Potts lattice spin models. We will study the critical phenomena of these percolation models on $\mathbb Z^2$ for $q \geq 1$. The goal is to prove that the phase transition is continuous for $1 \leq q \leq 4$ and discontinuous for $q>4$.
Syllabus:
Potts models and FK percolation.
Baxter-Kelland-Wu coupling with 6V.
Discontinuity when $q>4$.
Continuity when $1 \leq q \leq 4$.