  We study vicinal crystal surfaces within the terrace-step-kink model on a
discrete lattice. Including both a short-ranged attractive interaction and a
long-ranged repulsive interaction arising from elastic forces, we discover a
series of phases in which steps coalesce into bunches of $n_b$ steps each. The
value of $n_b$ varies with temperature and the ratio of short to long range
interaction strengths. For bunches with large number of steps, we show that, at
T=0, our bunch phases correspond to the well known periodic groove structure
first predicted by Marchenko. An extension to $T>0$ is developed. We propose
that the bunch phases have been observed in very recent experiments on Si
surfaces, and further experiments are suggested. Within the context of a
mapping of the model to a system of bosons on a 1D lattice, the bunch phases
appear as quantum n-mers.
