  The two-dimensional Terry-Horton equation is shown to exhibit the Dimits
shift when suitably modified to capture both the nonlinear enhancement of
zonal/drift-wave interactions and the existence of residual Rosenbluth-Hinton
states. This phenomenon persists through numerous simplifications of the
equation, including a quasilinear approximation as well as a four-mode
truncation. It is shown that the use of an appropriate adiabatic electron
response, for which the electrons are not affected by the flux-averaged
potential, results in an $\boldsymbol{E}\boldsymbol{\times}\boldsymbol{B}$
nonlinearity that can efficiently transfer energy nonlocally to length scales
on the order of the sound radius. The size of the shift for the nonlinear
system is heuristically calculated and found to be in excellent agreement with
numerical solutions. The existence of the Dimits shift for this system is then
understood as an ability of the unstable primary modes to efficiently couple to
stable modes at smaller scales, and the shift ends when these stable modes
eventually destabilize as the density gradient is increased. This nonlocal
mechanism of energy transfer is argued to be generically important even for
more physically complete systems.
