Broad Histogram Simulation: Microcanonical Ising Dynamics

We revisit here a new Monte Carlo approach, namely the Broad Histogram Method. It is based on two quantities, the numbers N_up and N_dn of potential modifications which could be performed starting from the system's current state, increasing or decreasing its energy E, respectively. Thus, the energy degeneracy g(E) can be directly determined from the microcanonical averages <N_up(E)> and <N_dn(E)> of these two quantities. This method was first tested by sampling states from a random walk along the energy axis, for which the control of possible correlations between successive averaging states is not an easy task. Neverthless, the resulting microcanonical averages could not depend upon the particular dynamics used to sample the Markovian chain of averaging states. Here, we test the same method within an alternative dynamics for which the quoted control becomes trivial.