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Applying Feynman diagrammatics to non-fermionic strongly correlated modelswith local constraints might seem generically impossible for two separatereasons: (i) the necessity to have a Gaussian (non-interacting) limit on top ofwhich the perturbative diagrammatic expansion is generated by Wick's theorem,and (ii) the Dyson's collapse argument implying that the expansion in powers ofcoupling constant is divergent. We show that for arbitrary classical latticemodels both problems can be solved/circumvented by reformulating thehigh-temperature expansion (more generally, any discrete representation of themodel) in terms of Grassmann integrals. Discrete variables residing on eitherlinks, plaquettes, or sites of the lattice are associated with the Grassmannvariables in such a way that the partition function (and correlations) of theoriginal system and its Grassmann-field counterpart are identical. Theexpansion of the latter around its Gaussian point generates Feynman diagrams. Aproof-of-principle implementation is presented for the classical 2D Isingmodel. Our work paves the way for studying lattice gauge theories by treatingbosonic and fermionic degrees of freedom on equal footing.

Grassmannization of classical models