  We show that quasiparticle excitations with irrational charge and irrational
exchange statistics exist in tight-biding systems described, in the continuum
approximation, by the Dirac equation in (2+1)-dimensional space and time. These
excitations can be deconfined at zero temperature, but when they are, the
charge re-rationalizes to the value 1/2 and the exchange statistics to that of
"quartons" (half-semions).
