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Deformed exchange statistics is realized in terms of electronic operators.This is employed to rewrite Hubbard type lattice models for particles obeyingdeformed statistics (we refer to them as deformed models) as lattice models forelectrons. The resulting models show up gauge--like modulations in the hoppingprocesses, which induce long-range correlations in the lattice. The conditionsfor the Bethe ansatz solvability of the latter are interpreted as restrictionsimposed on the statistics to be compatible with the Bethe ansatz solvability ofthe deformed models. It is found that solvable deformed models are notunitarily equivalent to fermionic models if the exchange of particles with thesame spin-orientations is deformed. Statistics deformations, where the exchangerelation of two particles is influenced by the presence of other particles,cannot be realized by fermionic operators.Comment: 4 pages revtex; minor changes, references adde

Fermionic long-range correlations realized by particles obeying deformed statistics