  Relying on a recent progress made in studying bilinearly indexed (bli) random
processes in \cite{Stojnicnflgscompyx23,Stojnicsflgscompyx23}, the main
foundational principles of fully lifted random duality theory (fl RDT) were
established in \cite{Stojnicflrdt23}. We here study famous Hopfield models and
show that their statistical behavior can be characterized via the fl RDT. Due
to a nestedly lifted nature, the resulting characterizations and, therefore,
the whole analytical machinery that produces them, become fully operational
only if one can successfully conduct underlying numerical evaluations. After
conducting such evaluations for both positive and negative Hopfield models, we
observe a remarkably fast convergence of the fl RDT mechanism. Namely, for the
so-called square case, the fourth decimal precision is achieved already on the
third (second non-trivial) level of lifting (3-sfl RDT) for the positive and on
the fourth (third non-trivial) level of lifting (4-sfl RDT) for the
corresponding negative model. In particular, we obtain the scaled ground state
free energy $\approx 1.7788$ for the positive and $\approx 0.3279$ for the
negative model.
