Theory of Phase Transitions in 2D Systems

Part of the Springer Theses book series (Springer Theses)


The phase of a two-dimensional complex plasma can be defined, in the thermodynamical sense, by the Coulomb coupling parameter \(\Upgamma,\) the ratio of the average kinetic and potential energy, as it was introduced in  Sect. 2.3. Critical values \(\Upgamma_{c}\) at the point of the phase transition between the liquid and solid state in a two-dimensional system have been obtained in computer simulations of the liquid to solid transition of a 2D electron gas as \(\Upgamma_{c}=95\pm2\) [1]. Thouless [2] calculated it based on the dislocation mediated melting mechanism as \(\Upgamma_{c}=78\). This melting mechanism will be subject of the following chapter. A later experiment with 2D electron sheets [3] yielded a \(\Upgamma_{c}=137\pm15\) which is larger than the theoretical prediction, and close to the critical value for 3D systems of \(\Upgamma_{c,3D}=172\) as it was obtained in Monte-Carlo simulations of a one-component plasma (OCP) [4]. The last  Chap. 5 gave a simple method for the estimation of \(\Upgamma\) of a two-dimensional system of particles, if the particle coordinates are available with a high spatial resolution. Though observing \(\Upgamma\) during an experiment involving a phase transition could help to identify the respective phases and the point of phase transition, it gives no information on how this transition might work on a fundamental level. The next chapters will address the different theories attempting to explain the underlying mechanisms.


Burger Vector Order Transition Orientational Order Hexatic Phase Core Energy 
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© Springer-Verlag Berlin Heidelberg  2011

Authors and Affiliations

  1. 1.Max Planck Institute for Extraterrestrial PhysicsGarchingGermany

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