Efficient parallel tempering for first-order phase transitions.

We present a Monte Carlo algorithm that facilitates efficient parallel tempering simulations of the density of states g(E) . We show that the algorithm eliminates the supercritical slowing down in the case of the Q=20 and Q=256 Potts models in two dimensions, typical examples for systems with extreme first-order phase transitions. As recently predicted, and shown here, the microcanonical heat capacity along the calorimetric curve has negative values for finite systems.