Fourier Monte Carlo Implementation Guide

The Fourier Monte Carlo algorithm represents a powerful tool to study criticality in lattice spins systems. In par- ticular, the algorithm constitutes an interesting alternative to other simulation approaches for models with microscopic or effective long-ranged interactions. However, due to the somewhat involved implementation of the basic algorithmic machinery, many researchers still refrain from using Fourier Monte Carlo. It is the aim of the present article to lower this barrier. Thus, the basic Fourier Monte Carlo algorithm is presented in great detail with emphasis on providing ready-to-use formulas for the reader's own implementation.