Analysis of Monte Carlo simulations of Quantum Spin Models

The purpose of this project is to examine various models of quantum magnetism, such as the Ising and Potts models, using Monte Carlo simulations to study how they are affected by temperature, and to apply various statistical techniques to analyze the numerical data from both. The Ising model, in particular, is used to study the phase transition of a ferromagnet at a certain temperature, where quantum spins are represented as points on a square lattice with two possible states, while the Potts model generalizes the spins to a larger number of states. Throughout this project I will describe the spin models I used and compare different possible Monte Carlo algorithms. I will also explain how I analyzed the data near the phase transition, using techniques such as Akaike Information Criterion and finite-size scaling.