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Lifted directed-worm algorithm.

Hidemaro Suwa¹

¹Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan.

Physical Review. E

|December 23, 2022

Summary

A new lifted directed-worm algorithm enhances Markov chain Monte Carlo (MCMC) simulations. This nonreversible Markov chain method significantly improves sampling efficiency for complex models like the Ising model.

Area of Science:

Computational Physics
Statistical Mechanics
Algorithm Development

Background:

Markov chain Monte Carlo (MCMC) methods are crucial for simulating complex systems.
Reversible Markov chains can limit sampling efficiency in MCMC.
Nonreversible Markov chains offer potential performance improvements.

Purpose of the Study:

To apply the lifting technique to construct a nonreversible Markov chain for the directed-worm algorithm.
To optimize the directed-worm algorithm for enhanced sampling efficiency.
To demonstrate the performance of the lifted algorithm on the four-dimensional hypercubic lattice Ising model.

Main Methods:

Utilized the lifting technique to introduce stochastic flow and break detailed balance.
Optimized worm update transition probabilities using geometric allocation.

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Minimized worm backscattering probability to maximize stochastic flow.

Main Results:

The lifted directed-worm algorithm achieved sampling efficiencies 80x, 5x, and 1.7x higher than standard worm, Wolff cluster, and previous lifted worm algorithms, respectively.
Demonstrated significant performance gains for the four-dimensional hypercubic lattice Ising model.
Estimated the dynamic critical exponent (z) to be approximately 0 for worm and Wolff cluster updates.

Conclusions:

The lifted directed-worm algorithm offers a substantial improvement in MCMC sampling efficiency.
This technique is versatile and applicable to both classical and quantum systems.
Further research can explore its application in diverse scientific domains.