Help with Monte Carlo Wang-Landau JDoS

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The discussion focuses on the Wang-Landau algorithm's ability to capture the complete joint density of states for a magnetic perovskite with specific exchange interactions. It highlights that the convergence criterion, based on flatness testing after a set number of Monte Carlo steps, does not guarantee the identification of all possible microstates. A simple example illustrates the vast number of microstates in a 20x20 Ising model, emphasizing the impracticality of sampling all microstates within a reasonable timeframe. The conversation underscores the limitations of the WL algorithm in fully exploring the microstate space. Overall, the Wang-Landau method is efficient but may not encompass every microstate in complex systems.
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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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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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