Spontaneous symmetry breaking and the flat phase of crystalline membranes

Abstract

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.

9 pages, 3 Figures

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Cited by in corpus (7)

• Topological continuum charges of acoustic phonons in 2D
• The flat phase of polymerized membranes at two-loop order
• Scale without conformal invariance in membrane theory
• Three-loop order approach to flat polymerized membranes
• Effective Field Theory for Acoustic and Pseudo-Acoustic Phonons in Solids
• Auxiliary fields approach to shift-symmetric theories: the ${\phi }^4$ derivative theory and the crumpled-to-flat transition of membranes at two-loop order
• Renormalization group approach to the elastic properties of graphene bilayers