Fast, hierarchical, and adaptive algorithm for Metropolis Monte Carlo simulations of long-range interacting systems

Abstract

We present a fast, hierarchical, and adaptive algorithm for Metropolis Monte Carlo simulations of systems with long-range interactions that reproduces the dynamics of a standard implementation exactly, i.e., the generated configurations and consequently all measured observables are identical, allowing in particular for nonequilibrium studies. The method is demonstrated for the power-law interacting long-range Ising model with nonconserved order parameter and a Lennard-Jones system both in two dimensions. The measured runtimes support an average complexity $O(N\log N)$, where $N$ is the number of spins or particles. Importantly, prefactors of this scaling behavior are small, which in practice manifests in speedup factors larger than $10^4$. The method is general and will allow the treatment of large systems that were out of reach before, likely enabling a more detailed understanding of physical phenomena rooted in long-range interactions.

References in corpus (8)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Accurate estimate of the critical exponent $\nu$ for self-avoiding walks via a fast implementation of the pivot algorithm
• Phase diagram and critical exponents of a dissipative Ising spin chain in a transverse magnetic field
• Order-N Cluster Monte Carlo Method for Spin Systems with Long-range Interactions
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Kibble-Zurek scaling in quantum speed limits for shortcuts to adiabaticity
• Simulated quantum annealing as a simulator of non-equilibrium quantum dynamics
• Kinetics of the Two-dimensional Long-range Ising Model at Low Temperatures

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• Markov-chain sampling for long-range systems without evaluating the energy
• Stochastic parameter optimization analysis of dynamical quantum critical phenomena in long-range transverse-field Ising chain
• Comparison of the clock, stochastic cutoff, and Tomita Monte Carlo methods in simulating the dipolar triangular lattice at criticality
• Rejection-free Glauber Monte Carlo for the 2D Random Field Ising Model via Hierarchical Probabilistic Counters
• Crossover in the Ordered Phase in the Non-Mermin-Wagner-Hohenberg Regime of Spin Models with Long-Range Coupling
• Harnessing finite-size effects to gauge aging in the $2D$ Ising model