Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2007-10-05
J. Phys. Soc. Jpn. 77, 024004 (2008)
Physics
Condensed Matter
Disordered Systems and Neural Networks
18 pages, 9 figures, 1 figure and 1 reference are added
Scientific paper
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.
Matsubara Fumitaka
Sasaki Munetaka
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