Hexatic phase

The hexatic phase is a phase that is between the solid and the isotropic liquid phases in two dimensional systems of particles. It is characterized by two order parameters: a short-range positional and a quasi-long-range orientational (sixfold) order. More generally, a hexatic is any phase that contains sixfold orientational order, in analogy with the nematic phase (with twofold orientational order).

The existence of the hexatic phase was proposed by John Michael Kosterlitz and David J. Thouless as well as Bertrand Halperin, David Robert Nelson and A. P. Young in theoretical studies about melting in two dimensions. They proposed two phase transitions by binding of topological defects (dislocation and declination). The first transition occurs when the solid (quasi-long-range positional order, long-range orientational order) undergoes a dislocation unbinding transition to the hexatic phase (short-range positional order, quasi-long-range orientational order). The second transition is the disclination unbinding transition which transforms the hexatic phase into an isotropic phase (short-range positional and orientational order).

See also

• XY model
• Kosterlitz-Thouless transition

References

• J.M. Kosterlitz & D.J. Thouless: Long Range Order and Metastability in Two–Dimensional Solids and Superfluids. J. Phys. C 5, L124 (1972)
• J.M. Kosterlitz & D.J. Thouless: Ordering Metastability, and Phase Transitions in Two–Dimensional Systems. J. Phys. C 6, 1181 (1973)
• J.M. Kosterlitz: The critical properties of the two-dimensional XY model. J . Phys. C 7, 1046 (1974)
• D.R. Nelson & J.M. Kosterlitz: Universal Jump in the Superfluid Density of Two-Dimensional Superfluids. Phys. Rev. Lett. 39, 1201 - 1205 (1977)
• B.I. Halperin & D.R. Nelson: Theory of Two-Dimensional Melting. Phys. Rev. Lett. 41, 121 - 124 (1978)
• D.R. Nelson & B.I. Halperin: Dislocation-mediated melting in two dimensions. Phys. Rev. B 19, 2457 - 2484 (1979)
• A.P. Young: Melting and the vector Coulomb gas in two dimensions. Phys. Rev. B 19, 1855 - 1866 (1979)
• A. Jaster: The hexatic phase of the two-dimensional hard disks system. Phys. Lett. A 330, 120-125 (2004)