Model and method

Classical spin Hamiltonian

Magnetic systems simulated using 𝕍egas are modeled by the classical Heisenberg model. The Heisenberg spin Hamiltonian, which includes the exchange, anisotropy and applied field interactions, is given by

where $J_{ij}$ is the exchange interaction constant between sites $i$ and $j$, $B$ and $\mathbf{n}_{i}$ are the magnetic field intensity and direction of site $i$, respectively, $\mu_{s}$ is the atomic magnetic moment, $\mathbf{S}_{i}$ and $\mathbf{S}_{j}$ are the spin moment directions of sites $i$ and $j$, respectively, and $\mathcal{H}_{ani}$ is the anisotropy term. The anisotropy term can take the form of uniaxial anisotropy or cubic anisotropy.

Monte Carlo Metropolis algorithm

𝕍egas simulates the time evolution of a classical spin magnetic system using the Monte Carlo Metropolis algorithm, where new configurations of a system are generated from a previous state using a transition probability. Different spin update policies are implemented in 𝕍egas, including a highly efficient adaptive move.

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