New renormalization equations for the Kosterlitz-Thouless transition

Abstract

A new set of renormalization equations for the two-dimensional Coulomb gas is derived and solved numerically. These equations give a new picture of the Kosterlitz-Thouless transition. A new temperature $T^{\mathrm{*}}$ is found. Above $T^{\mathrm{*}}$ the value of the dielectric constant at the transition is ${\epsilon }_c$=1/(4$T_c$) as before whereas below $T^{\mathrm{*}}$ the new result ${\epsilon }_c$$T_c$) is obtained. The singular behavior at $T^{\mathrm{*}}$ is explored. The results are translated into a renormalization-group flow diagram. An interesting consequence is that the universal jump prediction for the Kosterlitz-Thouless transition turns into a nonuniversal jump prediction for critical temperatures below $T^{\mathrm{*}}$.