Phase separations are best studies with this method. Two separate
boxes are used, and in addition to particle moves and volume changes
a transfer of particles between the boxes is permitted.
To achieve constant and equal temperature, pressure, and chemical
potential in both boxes the following procedure (due to Panagiotopoulos)
Let be the box volumes, with a constant . The
particle numbers are , again with a constant total of
Choose a particle in one of the boxes and perform a trial move
in the usual manner.
Compute the energy difference between the trial configuration and
the given one:
Accept or reject the trial configuration with probability
Repeat this basic MC step for a number of particles; usually all
particles in both boxes are treated in sequence.
Now perform a trial volume change
; since the total volume
is conserved the volume must change by .
In each box all particle coordinates are (implicitely) scaled by
which entails a change in energy of .
Compute the total enthalpy change
noting that the contributions to from each box cancel
each other (since
Accept/reject the volume exchange according to
Now follows the particle transfer step:
Choose one of the boxes with equal probabilites. Choose any of
the particles in box , remove it, and place it at an arbitrary position
in the other box, . The total Gibbs potential then changes according to
Note that the contributions from the chemical potential cancel since
Accept/reject the particle transfer according to
[to be extended...]
F. J. Vesely / University of Vienna