  Crystalline membranes are one of the rare examples of bidimensional systems
in which long-range order can stabilise an ordered phase in the thermodynamic
limit. By a careful analysis of the Goldstone modes counting, we propose a
symmetry breaking mechanism associated with the generation of the flat phase
and show how it highlights the crucial role played by the crystalline lattice
in the establishment of long-range order in these objects. Comparison with
other symmetry breaking mechanisms in membrane physics is also used to unveil
the links between symmetry breaking patterns and the physical properties of the
flat phase.
