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

Bertrand Halperin

Bertrand I. Halperin is the Hollis Professor of Mathematics and Natural Philosophy at the physics department of Harvard University.He grew up in Crown Heights, Brooklyn. He attended Harvard University , and did his graduate work at Berkeley with John J. Hopfield .In the 1970s, he, together with...

, David R. Nelson and A. P. Young in theoretical studies about melting in two dimensions. They proposed two phase transition

Phase transition

A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....

s by
binding of topological defect

Topological defect

In mathematics and physics, a topological soliton or a topological defect is a solution of a system of partial differential equations or of a quantum field theory homotopically distinct from the vacuum solution; it can be proven to exist because the boundary conditions entail the existence of...

s (dislocation and declination). The first transition occurs when the solid (quasi-long-range positional order, long-range orientational order) undergoes a dislocation

Dislocation

In materials science, a dislocation is a crystallographic defect, or irregularity, within a crystal structure. The presence of dislocations strongly influences many of the properties of materials...

 unbinding transition to the hexatic
phase (short-range positional order, quasi-long-range orientational order). The second transition is the disclination

Disclination

A disclination is a line defect in which rotational symmetry is violated. In analogy with dislocations in crystals, the term, disinclination, for liquid crystals first used by F. C. Frank and since then has been modified to its current usage, disclination.It is a defect in the orientation of...

unbinding transition which transforms the hexatic phase into an isotropic phase (short-range positional and orientational order).