GPU-accelerated Monte Carlo simulations of anisotropic Heisenberg ferromagnets

TL;DR

This paper introduces a GPU-accelerated Monte Carlo simulation method for anisotropic Heisenberg ferromagnets, achieving significant speedups and enabling large-scale, atomistic-level magnetic state simulations of complex nanostructures.

Contribution

The paper presents a GPU implementation of Monte Carlo simulations for the 3D anisotropic Heisenberg model, vastly improving computational efficiency and scalability.

Findings

Achieves two orders of magnitude speedup over traditional methods.

Enables simulation of systems with up to 10^8 spins on a single GPU.

Allows realistic modeling of large magnetic nanostructures.

Abstract

The Monte Carlo method is a powerful technique for computing thermodynamic magnetic states of otherwise unsolvable spin Hamiltonians, but the method becomes computationally prohibitive with increasing number of spins and the simulation of real materials and nanostructures is cumbersome. This paper presents the acceleration of Monte Carlo simulations of the three-dimensional anisotropic Heisenberg model on Graphics-Processing Units (GPU). The GPU implementation of the method presented here provides an acceleration of two orders of magnitude over conventional implementations and enables the simulation of large systems, with any crystal lattice, containing up to $10^8$ spins on a single GPU. This offers the possibility to simulate complex structures and devices that are hundreds of nanometers in size in order to compute their magnetic state at finite temperature with atomistic resolution.