Sym4state.jl: An efficient computation package for magnetic materials

Exploring magnetic configurations of magnets often involves utilizing the four-state method to obtain the magnetic interaction matrix, and Monte Carlo method to simulate spin textures and phase transition processes. However, computing the interaction matrix between magnetic atoms using the four-state method requires plenty of individual calculations. Despite manual simplifying the number of individual calculations based on material's symmetry is possible, there remains a necessity for an automated approach to streamline the process for high-throughput screening of magnetic materials. Meanwhile, the traditional sequential Monte Carlo simulation encounters challenges of low efficiency and long time consuming in dealing with large systems. Furthermore, the prior parallelism in the Heisenberg model was limited to parallel computation of the system's energy or run several replicas in parallel. Hence, in our pursuit of comprehensive parallelization for the Heisenberg model, we have introduced a novel adaptation of the checkerboard algorithm, enabling a fully parallelizable simulation of the Heisenberg model. To address these problems, we have developed Sym4state.jl, a program specifically designed to simplify the computation of magnetic interaction matrix and simulate spin textures under various environmental conditions. This program, available as a Julia package, can be freely accessed at https://github.com/A-LOST-WAPITI/Sym4state.jl.