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Fast algorithm to calculate density of states.

R E Belardinelli¹, V D Pereyra

¹Departamento de Física, Laboratorio de Ciencias de Superficie, Universidad Nacional de San Luis, CONICET, Chacabuco 917, 5700 San Luis, Argentina.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 16, 2007

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This study introduces a novel algorithm for calculating the density of states, improving upon the Wang-Landau method. The new approach avoids error saturation, providing a more accurate density of states calculation for complex systems.

Area of Science:

Computational Physics
Statistical Mechanics

Background:

The Wang-Landau method is a widely used Monte Carlo approach for determining the density of states.
Traditional implementations can suffer from error saturation, limiting accuracy for large systems or long simulations.

Purpose of the Study:

To introduce a modified Wang-Landau algorithm that overcomes the limitations of previous methods.
To improve the accuracy and efficiency of density of states calculations.

Main Methods:

Development of a new algorithm based on independent random walks in restricted energy ranges.
Modification of the density of states using a time-dependent function F(t) proportional to t^-1.
Analysis of the asymptotic behavior of the calculated density of states.

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Main Results:

The modified algorithm shows the calculated density of states, gm(E,t), asymptotically approaches the exact value g(ex)(E) with an error proportional to t^-1/2.
This asymptotic behavior effectively avoids the saturation of the error.
The interface growth of the energy histogram was found to belong to the random deposition universality class.

Conclusions:

The proposed algorithm offers a significant improvement over the standard Wang-Landau method for density of states calculations.
The findings provide a more robust method for studying complex systems in statistical mechanics and computational physics.