Funnel hopping Monte Carlo: An efficient method to overcome broken ergodicity

Area of Science:

• Computational physics
• Statistical mechanics
• Chemical thermodynamics

Background:

• Monte Carlo (MC) simulations are vital for studying atomic system thermodynamics.
• Ergodic sampling is often limited by high energy barriers in configuration space.
• Existing MC extensions can be computationally expensive or rely on approximations.

Purpose of the Study:

• To develop a novel, efficient, and exact method for overcoming sampling limitations in MC simulations.
• To address the challenge of high energy barriers in atomic system simulations.
• To improve the convergence speed of thermodynamic property investigations.

Main Methods:

• Proposed Funnel Hopping Monte Carlo (FHMC), inspired by smart darting but more efficient.
• Utilized Gaussian mixtures to approximate Boltzmann distributions around energy minima.
• Developed FHMC to facilitate direct jumps between different energy funnels.
• Integrated FHMC with parallel tempering for enhanced performance.

Main Results:

• FHMC demonstrated superior efficiency in overcoming energy barriers compared to conventional methods.
• The method successfully sampled complex energy landscapes, exemplified by Lennard-Jones clusters.
• FHMC significantly reduced the number of simulation steps required for convergence.
• Integration with parallel tempering further accelerated the simulation process.

Conclusions:

• FHMC provides an exact and computationally efficient solution for ergodic sampling challenges in MC simulations.
• The method is particularly effective for systems with complex, multi-funnel energy landscapes.
• FHMC offers a significant improvement for investigating thermodynamic properties of atomic systems, reducing computational cost and time.