  Monte Carlo switching moves ("perturbations") are defined between two or more
classical Hamiltonians sharing a common ground-state energy. The ratio of the
density of states (DOS) of one system to that of another is related to the
ensemble averages of the microcanonical acceptance probabilities of switching
between these Hamiltonians, analogously to the case of Bennett's acceptance
ratio method for the canonical ensemble [C. H. Bennett, J. Comput. Phys., 22,
245 (1976)]. Thus, if the DOS of one of the systems is known, one obtains those
of the others and, hence, the partition functions. As a simple test case, the
vapor pressure of an anharmonic Einstein crystal is computed, using the
harmonic Einstein crystal as the reference system in one dimension; an
auxiliary calculation is also performed in three dimensions. As a further
example of the algorithm, the energy dependence of the ratio of the DOS of the
square-well and hard-sphere tetradecamers is determined, from which the
temperature dependence of the constant-volume heat capacity of the square-well
system is calculated and compared with canonical Metropolis Monte Carlo
estimates. For these cases and reference systems, the perturbation calculations
exhibit a higher degree of convergence per Monte Carlo cycle than Wang-Landau
(WL) sampling, although for the one-dimensional oscillator the WL sampling is
ultimately more efficient for long runs. Last, we calculate the vapor pressure
of liquid gold using an empirical Sutton-Chen many-body potential and the ideal
gas as the reference state. Although this proves the general applicability of
the method, by its inherent perturbation approach, the algorithm is suitable
for those particular cases where the properties of a related system are well
known.
