  In conventional well-known derivation methods for the adaptive
Thouless-Anderson-Palmer (TAP) free energy, special assumptions that are
difficult to mathematically justify except in some mean-field models, must be
made. Here, we present a new adaptive TAP free energy derivation method. Using
this derivation technique, without any special assumptions, the adaptive TAP
free energy can be simply obtained as a high-temperature expansion of the Gibbs
free energy.
