%0 Journal Article
%T Stochastic Cutoff Method for Long-Range Interacting Systems
%A Munetaka Sasaki
%A Fumitaka Matsubara
%J Physics
%D 2007
%I arXiv
%R 10.1143/JPSJ.77.024004
%X A new Monte-Carlo method for long-range interacting systems is presented. This method consists of eliminating interactions stochastically with the detailed balance condition satisfied. When a pairwise interaction $V_{ij}$ of a $N$-particle system decreases with the distance as $r_{ij}^{-\alpha}$, computational time per one Monte Carlo step is ${\cal O}(N)$ for $\alpha \ge d$ and ${\cal O}(N^{2-\alpha/d})$ for $\alpha < d$, where $d$ is the spatial dimension. We apply the method to a two-dimensional magnetic dipolar system. The method enables us to treat a huge system of $256^2$ spins with reasonable computational time, and reproduces a circular order originated from long-range dipolar interactions.
%U http://arxiv.org/abs/0710.1177v2