  We study two-dimensional triangular-network models, which have degenerate
ground states composed of straight or randomly-zigzagging stripes and thus
sub-extensive residual entropy. We show that attraction is responsible for the
inversion of the stable phase by changing the entropy of fluctuations around
the ground-state configurations. By using a real-space shell-expansion method,
we compute the exact expression of the entropy for harmonic interactions, while
for repulsive harmonic interactions we obtain the entropy arising from a
limited subset of the system by numerical integration. We compare these results
with a three-dimensional triangular-network model, which shows the same
attraction-mediated selection mechanism of the stable phase, and conclude that
this effect is general with respect to the dimensionality of the system.
