Exchange Monte Carlo, equilibrium phase

Bolhuis and Frenkel have studied the phase behavior of a mixture of hard spheres and hard rods. In particular, Bolhuis and Frenkel used Gibbs-ensemble simulations to determine the vapor-liquid coexistence curve. In a Gibbs-ensemble simulation one simulates two boxes that are kept in equilibrium with each other via Monte Carlo rules. In this case the gas box has as a low density of hard spheres and the liquid box has a high density of spheres. Similarly to the phase equilibrium calculation of linear alkanes, the exchange step, in which particles are exchanged between the two boxes, is the bottleneck of the simulation. For example, the insertion of a sphere into the gas phase would almost always fail because of overlaps with some of the rods. Bolhuis and Frenkel have used the following scheme to make this exchange possible ... 

Particle exchanges, in order to achieve chemical equilibrium between the phases. We consider two simultaneous grand canonical Monte Carlo moves for the two systems in lV T and ensembles. 

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