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Multidimensional stochastic approximation Monte Carlo
Sergey V Zablotskiy1, Victor A Ivanov1, Wolfgang Paul2
1Faculty of Physics, Moscow State University, Moscow 119991, Russia.
Physical Review. E
|July 15, 2016
Summary
Stochastic Approximation Monte Carlo (SAMC) is generalized to compute multidimensional probability distributions, enabling systematic coarse-graining and renormalization group steps for statistical mechanical models.
Area of Science:
- Statistical Mechanics
- Computational Physics
- Computational Chemistry
Background:
- Stochastic Approximation Monte Carlo (SAMC) is a powerful flat-histogram method for determining the density of states g(E).
- Accurate determination of densities of states is crucial for understanding complex systems.
Purpose of the Study:
- Generalize SAMC for multidimensional probability distributions of macroscopic variables.
- Establish SAMC as a systematic method for coarse-graining and renormalization group transformations.
- Investigate the application to polymer models and analyze multidimensional densities of states.
Main Methods:
- Generalization of the Stochastic Approximation Monte Carlo (SAMC) method.
- Formulation of Kadanoff block spin transformation within the SAMC framework.
- Application to polymer models and analysis of two-dimensional densities of states g(E1, E2).
Main Results:
- Demonstrated generalization of SAMC for multidimensional probability distributions.
- Established a systematic approach for coarse-graining and renormalization group steps.
- Provided insights into obtaining microcanonical densities of states from multidimensional ones, highlighting potential pitfalls.
Conclusions:
- The generalized SAMC method offers a powerful tool for coarse-graining and renormalization in statistical mechanics.
- This approach facilitates the study of complex systems by simplifying their description.
- Careful consideration is needed when deriving microcanonical densities from multidimensional ones.
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