Replica Limit vs. thermodynamic limit

[beheiger]

[[Mod. note -- I apologise to the author and to s.p.r readers for
the long delay in approving this posting, which was originally dated
Tue, 10 Nov 2009 18:03:35 +0100. The delay was due to a mixup on
my part in saving the incoming message to the wrong mailbox.
-- jt]]

Hi there,

in the theory of quenched disorder in statistical systems
(random field spin models, spin glasses, etc.) a very popular
approach is the so-called replica trick, where one passes
from the ordinary partition function of the system at a given
realization of the disorder to a fictious system of n coupled
replicas. In many cases it is then possible to obtain an effective
Hamiltonian for this replica system, such that it can be formally
treated like a single system. After having computed the thermodynamic
properties of interest as a function of n, the results must be
analytically continued to the limit n->0.

Performing this limit is delicate, however. In particular, I
have read that it does not commute with the thermodynamic limit,
at least at low temperatures. Can anyone tell me more about this?

Thanks in advance for any help,

Andy