If you're really interested in free energy differences, check out Arjun Acharya's thesis, Free Energy differences: Representations, estimators, and sampling strategies (also on arxiv). The review chapter covers several methods, but most of the thesis deals with the Phase Mapping technique, which increases the overlap between phases. It does not eliminate the problem entirely, however, and many of the other methods can be used to deal with the remaining issues.
[Edit 2/27/06: updated links from comments, and revised the entry]
2 comments:
Editing the entry apparently deleted the comments (D'oh!)
Pasting them back in:
Hi,
Accidentally came across this site and saw my thesis on it. The university will probably take down the website eventually. More permanent link to the thesis can be found at:
http://arxiv.org/abs/cond-mat/0409613
Best Regards,
Arjun
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Or alternatively
http://www.ph.ed.ac.uk/cmatter/cgi-bin/archive/show.cgi?db=people&id=arjun
Arjun
Note that for first order structural phase transitions, the typical problems
associated with visiting the regions of configuration of BOTH phases in a single
run metropolis simulation can be overcome via a variety of techniques.
One option is to combine the phase mapping technique with the sampling
of a non-gibbsian distribution (which is not the equilibrium distribution of
the phase in question). The latter has
its origins in the work of Torrie and Valleau and Bennet. For further references on
such techniques, also refer to :
Extended Ensemble Monte Carlo by Yukito Iba
http://www.arxiv.org/abs/cond-mat/0012323
Computational strategies for mapping equilibrium phase diagrams by A.D. Bruce, N.B. Wilding
http://www.arxiv.org/abs/cond-mat/0210457
Note also that an alternative is to use thermodynamic integration for each phase
seperately, where the integration parameter is the (inverse) termperature. At sufficiently
low temperatures one knows that, in the classical framework, each phase is harmonic. Hence the
free energy can be determined exactly, since the free energy in the harmonic limit
may be computed exactly via the dynamical matrix. In this way one
may compute the absolute free energy of each phase seperately. Note that in the quantum mechanical
case, this cannot always be done since the presence of zero point motion (heisenbergs uncertainty
priciple), means that anharmonic effects MAY be present even at absolute zero.
Arjun
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