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The Monte Carlo method is a powerful technique for computing thermodynamicmagnetic states of otherwise unsolvable spin Hamiltonians, but the methodbecomes computationally prohibitive with increasing number of spins and thesimulation of real materials and nanostructures is cumbersome. This paperpresents the acceleration of Monte Carlo simulations of the three-dimensionalanisotropic Heisenberg model on Graphics-Processing Units (GPU). The GPUimplementation of the method presented here provides an acceleration of twoorders of magnitude over conventional implementations and enables thesimulation of large systems, with any crystal lattice, containing up to $10^8$spins on a single GPU. This offers the possibility to simulate complexstructures and devices that are hundreds of nanometers in size in order tocompute their magnetic state at finite temperature with atomistic resolution.

GPU-accelerated Monte Carlo simulations of anisotropic Heisenberg ferromagnets