Efficient Predecision Scheme for Metropolis Monte Carlo Simulation of Long-Range Interacting Lattice Systems

Area of Science:

• Computational Physics
• Statistical Mechanics
• Condensed Matter Physics

Background:

• Metropolis Monte Carlo simulations are crucial for studying lattice models.
• Long-range interactions in these models often lead to high computational complexity.
• Efficient simulation methods are needed to explore complex physical phenomena.

Purpose of the Study:

• To introduce a fast and general predecision scheme for Metropolis Monte Carlo simulations.
• To reduce the computational complexity of simulating d-dimensional lattice models with long-range interactions.
• To enable broader applications and deeper understanding of long-range interactions in physics.

Main Methods:

• Developed a predecision scheme for Metropolis Monte Carlo (MC) simulations.
• Analyzed computational complexity for potentials V(r)=r^{-d-σ}.
• Implemented and tested the scheme on Ising, XY, and Edwards-Anderson spin-glass models.

Main Results:

• Reduced computational complexity from O(N^2) to O(N^{2-σ/d}) for σd.
• The scheme produces identical Markov chains to explicit summation methods.
• Demonstrated efficiency across various spin models.

Conclusions:

• The proposed predecision scheme offers significant computational advantages.
• Its generality and simplicity facilitate broad application in lattice model simulations.
• It enhances the study of long-range interactions, particularly in nonequilibrium systems.