This is my honors thesis from the same project as “Fourier Acceleration in the Linear Sigma Model with Spontaneous Symmetry Breaking”. In this project we explore using Fourier acceleration to address the problem of “Critical Slowing Down” in the Linear Sigma Model.

Lattice QCD usually uses the Hybrid-Monte Carlo (HMC) method to generate lattice configurations. However, this method has a problem called “Critical Slowing Down” near phase transitions, where the autocorrelations between adjacent lattice configurations become large. To combat this problem, Fourier acceleration was proposed, which tunes the masses in the HMC algorithm to optimally evolve each momentum mode.

In this paper, we investigate Fourier acceleration in the Linear Sigma Model, a scalar quantum field theory with a spontaneously broken O(4) symmetry. Additionally we propose a novel method to dynamically estimate the Fourier masses.