# Home

The concept of information is fundamental to our universe, and I will use my site to share some of the information that I know. My blog posts are on various topics (mostly physics/math) that I find fascinating and I hope that after reading them you will too!

“Somewhere, something incredible is waiting to be known.” – Carl Sagan

# Recent Posts

• ### Simulating Magnetism Part 4: The $q$-State Potts Model

In this post we’ll go over what the $q$-State Potts model is, how the Metropolis algorithm can be applied to it, and see the results of running simulations with it.

• ### An Interesting Problem

A few years ago one of my professors mentioned an interesting problem to me: take a charged particle located at $\mathbf{x}$ of charge $q$ confined to motion on a ring of radius $r$ with another charged particle at $\mathbf{x}’$ fixed at the bottom of the ring with a like charge $q’$. The charged particle that is allowed to move freely around the ring is subject to both the gravitational force as well as the Coulomb force generated by the electromagnetic interaction of the charges. In this post we’ll cover how to solve it and then animate it.

• ### Simulating Magnetism Part 3: Running an Ising Model Simulation

In this post we’ll cover how to implement an Ising model simulation using the previously discussed Metropolis algorithm. We will also see an annotated implementation of the Metropolis algorithm with some optimizations that help reduce the compute time. Once we have the simulation data we will plot it and analyze it for various temperatures and lattice sizes to see how the system behaves differently as those variables change.