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

• UFSJ
In summary, the conversation discusses the normalization of the JDoS (Joint Density of States) in the Wang-Landau algorithm. The individual is working with a bi-dimensional space of energy and magnetization in an Ising spin-lattice. The conversation also mentions the relevance of normalization in updating the estimate for the density of states and suggests generating the estimation non-normalized and normalizing after the algorithm is terminated. The term JDoS refers to the Joint Density of States.
UFSJ
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.

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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