  We introduce an urn model which describes spatial separation of sand. In this
dynamical model, in a certain range of parameters spontaneous symmetry breaking
takes place and equipartitioning of sand into two compartments is broken. The
steady-state equation for an order parameter, a critical line, and the
tricritical point on the phase diagram are found exactly. Master equation and
the first-passage problem for the model are solved numerically and the results
are used to locate first-order transitions. Exponential divergence of a certain
characteristic time shows that the model can also exhibit very strong
metastability. In certain cases characteristic time diverges as N^{z}, where N
is the number of balls and z=1/2 (critical line), 2/3 (tricritical point), or
1/3 (limits of stability).
