  The recent discovery that for large Hilbert spaces, almost all (that is,
typical) Hamiltonians have eigenstates that place small subsystems in thermal
equilibrium, has shed much light on the origins of irreversibility and
thermalization. Here we give numerical evidence that many-body lattice systems
generically approach typicality as the number of subsystems is increased, and
thus provide further support for the eigenstate thermalization hypothesis. Our
results indicate that the deviation of many-body systems from typicality
decreases exponentially with the number of systems. Further, by averaging over
a number of randomly-selected nearest-neighbor interactions, we obtain a
power-law for the atypicality as a function of the Hilbert space dimension,
distinct from the power-law possessed by random Hamiltonians.
