Efficient Monte Carlo Simulation of Ferromagnetic Spin Configuration*

Due to the long-range dipole-dipole interactions (DDI) in ferromagnets (FM), the time complexity of Monte Carlo (MC) simulation is order O(N²), in a FM system with N spins. Tradition trivial MC algorithm is unbearably computationally expensive, as the size of system N increases. To solve this dilemma, we introduce an efficient algorithm named stochastic cutoff (SCO) algorithm and reduce the time complexity of O(N*log N). In this talk, I will show our simulation results of spin configuration in FM with different shapes.

Considering the anisotropy of DDI in FM, shape anisotropy will affect the spin configuration. As a result in long thin ferromagnets, spins prefer to align parallel to the long side of ferromagnets. In addition, magnetic domains of flux-closure shape can be observed in ferromagnets. These two kinds of spin configuration is related to not only the competition of the nearest-neighbouring exchange interaction J and dipole-dipole interaction D, but also the shape of the ferromagnts. We simulate the spin configuration from a first-principle perspective and study the phase diagram of spin configuration with different system sizes and interaction constants.