UVictoria Discrete Math Seminar: Lily Reeves

A phase transition is a phenomenon in physics, chemistry, and other related fields where the macroscopic behavior of a system changes qualitatively when the tuning parameter (such as temperature) that governs local interactions is varied by a small amount through a critical value. A familiar example of a phase transition is the evaporation of water into steam when the temperature reaches the boiling point.

In statistical mechanics, percolation is a simple model that undergoes a phase transition. At the critical threshold, percolation exhibits fractal properties that prove to be a rich area of research. In this talk, I will give a high-level introduction to the dimension-dependence of critical phenomena for percolation on Euclidean lattices.