  Jammed particulate systems composed of various shapes of particles undergo
the jamming transition as they are compressed or decompressed. To date, sphere
packings have been extensively studied in many previous works, where
isostaticity at the transition and scaling laws with the pressure of various
quantities, including the contact number and the vibrational density of states,
have been established. Additionally, much attention has been paid to
nonspherical packings, and particularly recent work has made progress in
understanding ellipsoidal packings. In the present work, we study the dimer
packings in two dimensions, which have been much less understood than systems
of spheres and ellipsoids. We first study the contact number of dimers near the
jamming transition. It turns out that packings of dimers have "rotational
rattlers", each of which still has a free rotational motion. After correcting
this effect, we show that dimers become isostatic at the jamming, and the
excess contact number obeys the same critical law and finite size scaling law
as those of spheres. We next study the vibrational properties of dimers near
the transition. We find that the vibrational density of states of dimers
exhibits two characteristic plateaus that are separated by a peak. The
high-frequency plateau is dominated by the translational degree of freedom,
while the low-frequency plateau is dominated by the rotational degree of
freedom. We establish the critical scaling laws of the characteristic
frequencies of the plateaus and the peak near the transition. In addition, we
present detailed characterizations of the real space displacement fields of
vibrational modes in the translational and rotational plateaus.

Soft Condensed Matter