Mean-field, High T Expansion paper

This is a discussion on the 1991 paper on "How to expand around mean-field theory using high-temperature expansions" by Georges and Yedidia, http://www.iop.org/EJ/abstract/0305-4470/24/9/024". Published in the Journal of Physics. We will be adding questions, comments etc. and share/critique the paper.

Some questions:
1) do the Lagrange multipliers in Eq. 2 replace any general external field? I think the answer is yes.

2) How does one get -<U(Si -mi)> = 0 in Eq. A1.4?

3) How meaningful is it to go past the Onsager term or TAP equations?
 
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