A TESTBENCH FOR THE NESTED DIPOLE HYPOTHESIS OF KOSTERLITZ AND THOULESS

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 i..