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)
is used:
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:
, where
etc.
Accept or reject the trial configuration with probability
(6.5)
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
(6.6)
noting that the contributions to from each box cancel
each other (since
).
Accept/reject the volume exchange according to
(6.7)
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
(6.8)
Note that the contributions from the chemical potential cancel since
.
Accept/reject the particle transfer according to
(6.9)
[to be extended...]
F. J. Vesely / University of Vienna