Help with Monte Carlo Wang-Landau JDoS

  • #1
UFSJ
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Hi, guys.

I have tried to write a Wang-Landau JDoS algorithm to describe a magnetic perovskite with exchange interactions J1 = 1.66 and J2 = -1.16. Then, I have a simple question: in the WL algorithm, the obtained joint density of states must have all possible E x M microstates? Since the convergence criterion in WL is just the flatness test after some Monte Carlo steps (e.g., n * 10^6), it is not guaranteed that all microstates will be identified, correct???
 
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  • #2
It is not guaranteed that you constructed all microstates. So if that's what you meant by "[not] all microstates will be identified", then you are correct.

Simple example: A 20x20 Ising model has 2^400= 2.5*10^120 microstates. Generating 10^10 microstates per second (10 per nanosecond) would mean that you would need about 10^100 years to sample all microstates. A 2D WL run for such a model will probably take a couple of seconds, maybe minutes.
 
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Likes Tom.G and pbuk

1. What is Monte Carlo Wang-Landau JDoS?

Monte Carlo Wang-Landau JDoS (Joint Density of States) is a computational method used to estimate the density of states of a physical system. It is often used in statistical mechanics and material science to study the thermodynamic properties of complex systems.

2. How does Monte Carlo Wang-Landau JDoS work?

This method uses a sampling algorithm to explore the energy landscape of a system and obtain a probability distribution of energy states. The probability distribution is then used to calculate the density of states, which is a measure of how many energy states are available to the system at a given temperature.

3. What is the advantage of using Monte Carlo Wang-Landau JDoS?

The main advantage of this method is that it can accurately estimate the density of states for systems with a large number of degrees of freedom. It also allows for efficient exploration of the energy landscape and can be used to study phase transitions and critical phenomena in physical systems.

4. What are the limitations of Monte Carlo Wang-Landau JDoS?

One limitation is that it requires a large number of iterations to obtain accurate results, which can be computationally expensive. It also relies on the choice of a suitable sampling algorithm and can be sensitive to the initial conditions and parameters chosen.

5. How can Monte Carlo Wang-Landau JDoS be used in scientific research?

This method has been successfully used in many scientific studies, such as in the analysis of complex materials, protein folding, and phase transitions in physical systems. It can also be applied to other fields, such as machine learning and data analysis, to estimate the density of states of high-dimensional systems.

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