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arXiv · 0710.1177

Stochastic Cutoff Method for Long-Range Interacting Systems

Munetaka Sasaki·Fumitaka Matsubara
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Abstract

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 $r_{ij}^{-α}$, computational time per one Monte Carlo step is ${\cal O}(N)$ for $α\ge d$ and ${\cal O}(N^{2-α/d})$ for $α< d$, 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.

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Munetaka Sasaki, Fumitaka Matsubara. 2007-12-27. Stochastic Cutoff Method for Long-Range Interacting Systems. https://doi.org/10.1143/jpsj.77.024004

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