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.