  Inspired by the recent interest in the Sachdev-Ye-Kitaev (SYK) model we study
a class of multi-flavored one- and two-band fermion systems with no bare
dispersion. In contrast to the previous work on the SYK model that would
routinely assume spatial locality, thus unequivocally arriving at the so-called
'locally-critical' scenario, we seek to attain a spatially-dispersing
'globally-SYK' behavior. To that end, a variety of the Lorentz-(non)invariant
space-and/or-time dependent algebraically decaying interaction functions is
considered and some of the thermodynamic and transport properties of such
systems are discussed.
