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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Related to Help with Monte Carlo Wang-Landau JDoS

1. How do I implement Monte Carlo Wang-Landau JDoS?

To implement Monte Carlo Wang-Landau JDoS, you first need to understand the algorithm and its parameters. Then, you can write a code in a programming language of your choice (such as Python or C++) that follows the steps of the algorithm, including updating the density of states and performing the Monte Carlo sampling.

2. What are the advantages of using Monte Carlo Wang-Landau JDoS?

Monte Carlo Wang-Landau JDoS is advantageous because it allows for efficient sampling of the density of states, which can be useful for studying complex systems with multiple energy states. Additionally, it can help overcome the limitations of traditional Monte Carlo methods by reducing the computational cost of sampling rare states.

3. How do I choose the parameters for Monte Carlo Wang-Landau JDoS?

Choosing the parameters for Monte Carlo Wang-Landau JDoS involves tuning the flatness criterion and the modification factor. The flatness criterion determines when to update the density of states, while the modification factor controls the rate of updating. It is important to experiment with different parameter values to find the optimal settings for your specific system.

4. What are some common challenges when using Monte Carlo Wang-Landau JDoS?

Some common challenges when using Monte Carlo Wang-Landau JDoS include convergence issues, choosing appropriate initial conditions, and determining the optimal modification factor. It is important to carefully monitor the convergence of the algorithm and adjust the parameters accordingly to ensure accurate results.

5. Are there any resources available for learning more about Monte Carlo Wang-Landau JDoS?

There are several resources available for learning more about Monte Carlo Wang-Landau JDoS, including research papers, textbooks, and online tutorials. Additionally, there are software packages and libraries that implement the algorithm, which can serve as useful tools for understanding and applying Monte Carlo Wang-Landau JDoS in your research.

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