How to normalize the density of states in JDoS Wang-Landau?

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SUMMARY

The discussion focuses on normalizing the density of states (DoS) in the Joint Density of States (JDoS) using the Wang-Landau algorithm, specifically for the Ising model. The key point is that while updating the logarithm of the density of states, the ground state value must equal Q (Q = 2 for the Ising model). The participants emphasize that normalization is not necessary during the Monte Carlo steps, as only the relative density of states is considered, allowing for non-normalized generation followed by normalization post-algorithm completion.

PREREQUISITES
  • Understanding of the Ising model and its parameters, particularly ground state energy and magnetization.
  • Familiarity with the Wang-Landau algorithm for density of states calculations.
  • Knowledge of Monte Carlo methods in statistical mechanics.
  • Basic concepts of logarithmic functions and their application in density of states normalization.
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  • Research the implementation of the Wang-Landau algorithm in computational physics.
  • Explore methods for calculating the Joint Density of States (JDoS) in multi-dimensional systems.
  • Learn about the significance of ground state energy in statistical mechanics.
  • Investigate techniques for post-processing normalization of density of states data.
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Researchers and practitioners in computational physics, particularly those working with statistical mechanics, Monte Carlo simulations, and the Ising model. This discussion is beneficial for anyone looking to enhance their understanding of density of states normalization in complex systems.

UFSJ
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Hi guys.

I want some help understanding how I can make the normalization of the JDoS density of states (Ω[E,m]) in the Wang-Landau algorithm. When I am working with DoS (Ω[E]) I use the knowledge that the value of the density of states in the ground states must be
equal to Q (Q = 2 for the Ising model), that is, I make the update ln[Ω(E)] = ln[Ω(E)] - ln[Ω(Eground state )] + ln[2]. However, I don't know how to update the ln[Ω(E,m)] in the JDoS algorithm. I am working with a bi-dimensional space of energy (E) and magnetization (m) in an Ising spin-lattice.
 
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I assume that you talk about an Ising like model. If you sample in E and m, then the number of states with E_groundstate is one for m=+N and m=-N (where N is the number of spins total and m assumed to be in units of spins pointing up). The number of states with E_groundstate and any other magnetization is zero, which may actually become a problem for you if you do not handle this situation.

I think normalization is irrelevant for updating your estimate for the density of states (DOS). Your Monte-Carlo steps (assuming you do MC) only take the relative DOS into account, and the normalization drops out of the calculation. So you can just generate your DOS estimation non-normalized and normalize after the algorithm is terminated.

What is JDoS?
 

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