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Published on: January 15, 2016
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Nonconvergence of the Wang-Landau algorithms with multiple random walkers
R E Belardinelli1,2, V D Pereyra2
1Instituto de Física Aplicada (INFAP)-CONICET, San Luis, Argentina.
Physical Review. E
|June 15, 2016
Summary
Using multiple walkers in Monte Carlo simulations, like Wang-Landau (WL) and 1/t algorithms, improves error reduction up to a critical point. Increasing walkers beyond this point offers no further convergence benefits for density of states calculations.
Area of Science:
- Computational Physics
- Statistical Mechanics
Background:
- Entropic sampling Monte Carlo methods are crucial for calculating the density of states (DOS).
- Classical algorithms like Wang-Landau (WL) and 1/t can be enhanced using multiple random walkers.
Purpose of the Study:
- To investigate the convergence properties of entropic sampling Monte Carlo methods with multiple random walkers.
- To compare the efficiency and accuracy of the Wang-Landau (WL) and 1/t algorithms when using multiple walkers.
Main Methods:
- Modified Wang-Landau (WL) and 1/t algorithms employing m-independent random walkers.
- Application to the Ising model for DOS and critical temperature calculations.
- Application to multi-dimensional integration for calculating pi in a continuum approximation.
Main Results:
- Error in DOS calculation decreases as 1/sqrt(m), where m is the number of walkers.
- Error saturates beyond a critical number of walkers (m > m_x) for both algorithms.
- The 1/t algorithm demonstrates superior efficiency and accuracy compared to the WL algorithm for similar systems.
Conclusions:
- Increasing the number of walkers beyond a critical threshold (m_x) does not improve error reduction or guarantee convergence.
- The 1/t algorithm is a more efficient and accurate choice than the WL algorithm for density of states calculations with multiple walkers.
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