ISSN:
1572-9613
Keywords:
Kosterlitz-Thouless transition
;
Coulomb gas
;
renormalization equations
;
correlations
;
exact solution
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We consider the two-dimensional one-component plasma without a background and confined to a half-plane near a metal wall. The particles are also subjected to an external potential acting perpendicular to the wall with an inverse-power-law Boltzmann factor. The model has a known solvable isotherm which exhibits a Kosterlitz-Thouless-type transition from a conductive to an insulator phase as the power law is varied. This allows predictions of theoretical methods of analyzing the Kosterlitz-Thouless transition to be compared with the exact solution. In particular, we calculate the asymptotic density profile by resumming its low-fugacity expansion near the zero-density critical coupling in the insulator phase, and solving a mean-field equation deduced from the first BGY equation. Agreement with the exact solution is obtained. As the former calculation makes essential use of the nested dipole hypothesis of Kosterlitz and Thouless, the validity of this hypothesis is explicitly verified.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02184869
Permalink
