  Applying Feynman diagrammatics to non-fermionic strongly correlated models
with local constraints might seem generically impossible for two separate
reasons: (i) the necessity to have a Gaussian (non-interacting) limit on top of
which the perturbative diagrammatic expansion is generated by Wick's theorem,
and (ii) the Dyson's collapse argument implying that the expansion in powers of
coupling constant is divergent. We show that for arbitrary classical lattice
models both problems can be solved/circumvented by reformulating the
high-temperature expansion (more generally, any discrete representation of the
model) in terms of Grassmann integrals. Discrete variables residing on either
links, plaquettes, or sites of the lattice are associated with the Grassmann
variables in such a way that the partition function (and correlations) of the
original system and its Grassmann-field counterpart are identical. The
expansion of the latter around its Gaussian point generates Feynman diagrams. A
proof-of-principle implementation is presented for the classical 2D Ising
model. Our work paves the way for studying lattice gauge theories by treating
bosonic and fermionic degrees of freedom on equal footing.
