KTHNY theory

The KTHNY theory is a specific example of a defect-mediated melting theory, of which there are numerous other examples. In Section II.E we discuss some of the other 2D defect-mediated melting theories, including computer simulations of systems of interacting defects. 

The full KTHNY theory improves upon the simple instability theory presented above in several respects. Kosterlitz and Thouless recognized that the elastic constants of a solid containing thermally excited dislocation pairs are renormalized by the presence of such excitations, so that the coupling constant that appears in the above formula for the transition... 

In the remainder of this subsection, we describe the major assumptions and key results of the KTHNY theory. 

The KTHNY theory is based on linear continuum elastic theory [82], so that the statistical properties of the system are determined by the reduced elastic Hamiltonian... 

With this in mind, it is worthwhile to review the major assumptions and approximations of the KTHNY theory ... 

Because of its use of linear continuum elastic theory, the KTHNY theory would be expected to describe the solid phase much better than the liquid phase. Also, the KTHNY theory neglects anharmonic effects other than those due to topological defects. Nontopological anharmonic excitations may make a significant contribution to the properties of the solid and liquid phases, and may be important in determining the nature of the 2D melting transition. 

The earliest vacancy-mediated melting theories were essentially instability theories, which predicted the temperature at which the free energy of formation of vacancies becomes negative (an example of such arguments can be found in the section on KTHNY theory above). More recent theories (such as O Reilly s) view melting as a vacancy condensation transition. Vacancy-mediated melting theories have never enjoyed wide acceptance because the concept of a vacancy is ill-defined in the liquid phase, and because such theories seem to be inapplicable to substances that contract upon melting. 

A quantity of interest in the KTHNY theory of 2D melting is the so-called Halperin-Nelson order parameter,... 

It is interesting to contrast this melting model with the KTHNY theory. In the KTHNY theory, 2D melting is associated with the unbinding of a dilute gas of thermally generated, bound dislocation pairs,... 

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