6.3 Extended Gibbs ensemble MC

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 probabilities . 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:

(6.10) |

(6.11) |

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 .

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