Melting Transition in Two Dimensions

The two-dimensional melting transition of a lattice of point-like constituents proceeds in first order where dislocations and disclination separate in a single discontinuous transition. See here, and here.
If the lattice constituents are elongated, the disclinations are independent of the dislocations and there exist an independent material parameter the ANGULAR STIFFNESS. (here and here).
If this is sufficiently large, the transition separates into two continuous Berezinsky-Kosterlitz-Thouless-type of transitions. In the first, the dislocation-antidislocation pairs separate, in the second, the same thing happens to the disclination-antodisclination pairs here and here)
Everything is contained in the textbook

Hagen Kleinert: Gauge Fields in Condensed Matter, World Scientific, 1989.

Vol. II, STRESSES AND DEFECTS
Differential Geometry, Crystal Melting
pp. 743-1456, World Scientific, Singapore 1989
[ISBN 9971-50-210-0 & 9971-50-210-9 (paperback)]

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