Talk on percolation, universality and coarsening

Synopsis

After performing random walks through Differential Geometry, Quantum Mechanics, and Group Theory, it’s time to let some Statistical Mechanics percolate through you.

If we build a maze by randomly connecting corridors, what is the probability that an ant can wander forever without hitting a dead end? Or, in a forest, what is the minimum density of trees required before a small spark inevitably grows into an uncontainable wildfire? Questions like these lead us to Percolation Theory.

In this talk, we will begin by introducing the basic ideas of percolation and exploring various percolation models, highlighting their surprisingly broad range of applications beyond physics. We will then analyze the 1D percolation model, where the notions of critical points and critical exponents naturally emerge. At the critical threshold, we will see how purely geometric phase transitions arise and discuss Peierls’ argument, which provides bounds on such critical points. In the second half, we will explore the powerful concept of universality: the observation that systems which look completely different microscopically can exhibit identical behaviour near their critical point, provided they share the same symmetry and dimensionality. Finally, we will introduce the idea of coarse-graining and develop an intuitive understanding of the Renormalization Group (RG), connecting back to the themes of scaling and universality that run throughout percolation theory. The mathematical discussion in the talk will be kept at a basic level, with no prerequisites required!

Details of the session:

Speaker: Panchariya Chinmay Anil (3rd Year UG)
Date: 9th November (Sunday)
Time: 2:30 PM
Venue: F-08A, OPB