At higher densities the Gibbs ensemble MC method is plagued by a low
acceptance probability of particle insertion. To overcome this problem,
several authors suggested to combine the GEMC method with a kind of
``scaled particle'', or ``extended ensemble'' strategy.
In the following we will describe the procedure developed by
Strnad and Nezbeda (1999).
The basic idea of the extended ensemble is that in addition to the
states where a box contains or particles, there may be
a total of states in which one particle is incompletely coupled
to the system, having a smaller size, or potential coupling parameter
. For a complete definition of the extended ensemble,
weights have to be assigned, in an arbitrary manner, to the intermediate
box states. In the original work of Strnad and Nezbeda there was only one
intermediate state (), and the corresponding weight was set to
Generally, if all weights
are taken to be equal, they
cancel from the pertinent formulae. To keep things simple, we will therefore
assume equal weights. For the same reason we will take all trial
. Note, however, that the efficiency
of the method may be much enhanced by using non-uniform weights .
Instead of transferring a particle from box to in a single step,
it now undergoes a shrinking process through the intermediate sizes
before it is transferred to .
Strnad and Nezbeda suggested two possible implementations of their
method, denoted as EGE1 and EGE2:
EGE1: Particle in box is first shrunk to its smallest
size , then transferred to box , to be re-inflated there.
Let the energy difference in box between the states and
of the scaled particle be
The acceptance probability of a decoupling/coupling step is then
As soon as , the transfer from to is accepted with probability
where is the energy in box upon insertion of a scaled
particle in state .
We expect that the latter acceptance probability, which is so small in
the basic Gibbs ensemble MC, will be larger since only a minuscule
new particle is inserted in .
EGE2: A particle in box is shrunk simultaneously with
an inflation of another particle in box .
In a sample computation, Strnad and Nezbeda report that EGE2 shows
no higher efficiency than EGE1.
[to be completed... March 02]
Lit.: Strnad and Nezbeda, Mol.Simul. 22 (1999) 183
F. J. Vesely / University of Vienna