Cluster Monte Carlo and dynamical scaling for long-range interactions

Abstract

Many spin systems affected by critical slowing down can be efficiently simulated using cluster algorithms. Where such systems have long-range interactions, suitable formulations can additionally bring down the computational effort for each update from O($N^2$) to O($N\ln N$) or even O($N$), thus promising an even more dramatic computational speed-up. Here, we review the available algorithms and propose a new and particularly efficient single-cluster variant. The efficiency and dynamical scaling of the available algorithms are investigated for the Ising model with power-law decaying interactions.

submitted to Eur. Phys. J Spec. Topics

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• Finite-size scaling above the upper critical dimension
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• Bosonized one-dimensional quantum systems through enhanced event-chain Monte Carlo
• High-temperature partition functions and classical simulatability of long-range quantum systems
• Criticality of the magnon-bound-state hierarchy for the quantum Ising chain with the long-range interactions