  We develop and discuss the properties of a new class of lattice-based
avalanche models of solar flares. These models are readily amenable to a
relatively unambiguous physical interpretation in terms of slow twisting of a
coronal loop. They share similarities with other avalanche models, such as the
classical stick--slip self-organized critical model of earthquakes, in that
they are driven globally by a fully deterministic energy loading process. The
model design leads to a systematic deficit of small scale avalanches. In some
portions of model space, mid-size and large avalanching behavior is scale-free,
being characterized by event size distributions that have the form of
power-laws with index values, which, in some parameter regimes, compare
favorably to those inferred from solar EUV and X-ray flare data. For models
using conservative or near-conservative redistribution rules, a population of
large, quasiperiodic avalanches can also appear. Although without direct
counterparts in the observational global statistics of flare energy release,
this latter behavior may be relevant to recurrent flaring in individual coronal
loops. This class of models could provide a basis for the prediction of large
solar flares.
