Calculation of The Density of States
Interesting systems are in general complex, for instance compounds, biomolecules, polymers, etc. Because of the complexity of these systems the analytical calculation of the density of states is in most of the cases impossible. Computer simulations offer a set of algorithms to evaluate the density of states with a high accuracy. One of these algorithms is called the Wang and Landau algorithm.
Within the Wang and Landau scheme any previous knowledge of the density of states is required. One proceed as follows: the cost function (for example the energy) of the system is discretized. Each time the bin i is reached one update a histogram for the density of states, by
where f is called modification factor. As soon as each bin in the histogram is visited a certain number of times (10-15), the modification factor is reduced by some criterion, for instance,
where n denotes the n-th update step. The simulation finishes when the modification factor is less than a certain threshold, for instance .
The Wang and Landau algorithm has some advantages over other common algorithms such as multicanonical simulations and Parallel tempering, for instance, the density of states is obtained as the main product of the simulation. Additionally, Wang and Landau simulations are completely independent of the temperature. This feature allows to compute the density of states of systems with very rough energy landscape such as proteins.
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