The statistical mechanics of membranes

Mark J. Bowick, Alex Travesset

Research output: Contribution to journalArticlepeer-review

175 Scopus citations


The fluctuations of two-dimensional extended objects (membranes) is a rich and exciting field with many solid results and a wide range of open issues. We review the distinct universality classes of membranes, determined by the local order, and the associated phase diagrams. After a discussion of several physical examples of membranes we turn to the physics of crystalline (or polymerized) membranes in which the individual monomers are rigidly bound. We discuss the phase diagram with particular attention to the dependence on the degree of self-avoidance and anisotropy. In each case we review and discuss analytic, numerical and experimental predictions of critical exponents and other key observables. Particular emphasis is given to the results obtained from the renormalization group ε-expansion. The resulting renormalization group flows and fixed points are illustrated graphically. The full technical details necessary to perform actual calculations are presented in the Appendices. We then turn to a discussion of the role of topological defects whose liberation leads to the hexatic and fluid universality classes. We finish with conclusions and a discussion of promising open directions for the future.

Original languageEnglish (US)
Pages (from-to)255-308
Number of pages54
JournalPhysics Report
Issue number4-6
StatePublished - Apr 2001


  • Crumpling
  • Fluctuating geometries
  • Interfaces
  • Membrane
  • Polymerized membranes
  • Random surfaces
  • Statistical mechanics
  • Surfaces
  • Tethered membranes

ASJC Scopus subject areas

  • General Physics and Astronomy


Dive into the research topics of 'The statistical mechanics of membranes'. Together they form a unique fingerprint.

Cite this