Markov-chain sampling for long-range systems without evaluating the energy.

Area of Science:

• Computational physics
• Statistical mechanics
• Molecular dynamics

Background:

• Traditional methods for simulating long-range interacting particle systems often require approximations like cutoffs or complex algorithms (e.g., particle-mesh Ewald, fast multipole methods).
• These methods necessitate extrapolations and can be computationally intensive, especially for large systems like those in biomolecular simulations.

Purpose of the Study:

• To introduce and detail a class of cell-veto algorithms for native sampling of the Boltzmann distribution.
• To demonstrate that these algorithms can efficiently handle long-range interactions without approximations or cutoffs.

Main Methods:

• Review of past attempts at native Boltzmann distribution sampling within Markov-chain Monte Carlo.
• Detailed discussion and illustration of cell-veto algorithms, including pseudocode.
• Analysis of computational cost scaling with system size.

Main Results:

• Cell-veto algorithms allow native sampling of the Boltzmann distribution without approximations, extrapolations, or cutoffs.
• The computational effort per move remains constant regardless of system size, even for slowly decaying interactions like Coulombic forces.
• Worked-out examples and pseudocode are provided, with accompanying Python scripts in an open-source repository.

Conclusions:

• Cell-veto algorithms offer a significant advancement for simulating particle systems, particularly those with long-range interactions.
• These algorithms provide a computationally efficient and accurate alternative to traditional methods, with scalable performance.