Stochastic Cutoff Method for Long-Range Interacting Systems

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

18 pages, 9 figures, 1 figure and 1 reference are added

References in corpus (1)

• A New Monte Carlo Method and Its Implications for Generalized Cluster Algorithms

Cited by in corpus (14)

• Order-N Cluster Monte Carlo Method for Spin Systems with Long-range Interactions
• The correspondence between long-range and short-range spin glasses
• Study on Effects of Dipole-dipole Interactions in Nd_2Fe_{14}B thin film Based on Stochastic Cut-off Method with New Efficient Algorithm
• Phase diagram of the two-dimensional dipolar Heisenberg model with the Dzyaloshinskii-Moriya interaction and the Ising anisotropy
• Anisotropy-temperature phase diagram for the two-dimensional dipolar Heisenberg model with and without magnetic field
• An Efficient Monte-Carlo Method for Calculating Free-Energy in Long-Range Interacting Systems
• Temperature-field phase diagram of the two-dimensional dipolar Ising ferromagnet
• Reformulation of the Stochastic Potential Switching Algorithm and a Generalized Fourtuin-Kasteleyn Representation
• Critical temperature of site-diluted spin-1/2 systems with long-range ferromagnetic interactions
• Phase diagram of the dipolar Ising ferromagnet on a kagome lattice
• Parallelized Stochastic Cutoff Method for Long-Range Interacting Systems
• Theory of magnetic vortex crystals induced by electric dipole interactions
• Comparison of the clock, stochastic cutoff, and Tomita Monte Carlo methods in simulating the dipolar triangular lattice at criticality
• A Superparamagnetic State Induced by a Spin Reorientation Transition in Ultrathin Magnetic Films