An efficient method of spin dynamics for long-range interacting systems

We developed an efficient method for dynamical simulation, TQMC+SCO, which is useful for classical spin systems with long-range interactions.
The method incorporates the stochastic cutoff method (SCO), which is originally specialized for simulating equilibrium state, into the time quantified Monte Carlo (TQMC) method. By using TQMC+SCO, the computational time for the spin-update process is proportional to O(\beta N log N) no matter how complicated the lattice structure is.
We analytically proved that TQMC+SCO gives the same time evolution of the magnetization distribution as the stochastic Landau-Lifshitz-Gilbert (s-LLG) equation. In addition, we simulated a magnetization reversal process and confirmed that the result obtained by TQMC+SCO is in good agreement with that obtained by s-LLG.
In this presentation, we introduce TQMC+SCO and discuss why this method works.
We also present several examples, where TQMC+SCO can be a strong tool.