6.2 Gibbs ensemble MC

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)

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)

Accept/reject the particle transfer according to

(6.9)

F. J. Vesely / University of Vienna