**Authors**:
Alessandro Giuliani, Elliott H. Lieb

**Title:** *
Columnar Phase in Quantum Dimer Models
*

**Sommario**:*
The quantum dimer model, relevant for short-range resonant valence bond physics, is rigorously shown to have long range order in a
crystalline phase in the attractive case at low temperature and not too
large flipping term. This term flips horizontal dimer pairs to vertical
pairs (and vice versa) and is responsible for the word `quantum' in
the title. In addition to the dimers, monomers are also allowed. The
mathematical method used is `reflection positivity'. The model and
proof can easily be generalized to dimers or plaquettes in 3-dimensions.
*

Alessandro Giuliani

Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre,
00146 Roma Italy

giuliani@mat.uniroma3.it

Elliott H. Lieb

Departments of Mathematics and Physics, Jadwin Hall, Princeton University
Princeton 08544 NJ, USA

lieb@math.princeton.edu