Comments on “power-law falloff in the Kosterlitz-Thouless phase of a two-dimensional lattice Coulomb gas”

Abstract

A simple argument is presented by which one can show that the critical inverse temperatureβ _c of a two-dimensional Coulomb gas (standard or hard-core) with activityz satisfies$\beta _c \leqslant \mathop \beta \limits^ -$, where$\mathop \beta \limits^ - = \mathop \beta \limits^ - (z) \to (1 + \sqrt 3 ) 8\pi /(3 - \sqrt 3 )$ in the low-activity limit. Previous results yield$\mathop \beta \limits^ - (z) \to 24\pi$.