Difference of energy density of states in the Wang-Landau algorithm

Paying attention to the difference of density of states, Δln g(E) = ln g(E+ΔE) - ln g(E), we study the convergence of the Wang-Landau method. We show that this quantity is a good estimator to discuss the errors of convergence, and refer to the $1/t$ algorithm. We also examine the behavior of the 1st-order transition with this difference of density of states in connection with Maxwell's equal area rule. A general procedure to judge the order of transition is given.

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