ON THE ABSENCE OF INTERMEDIATE PHASES IN THE 2-DIMENSIONAL COULOMB GAS

For a simple, continuum two-dimensional Coulomb gas (with ''soft'' cut off), Gallavotti and Nicolo [J. Stat. Phys. 38:133-156 (1985)] have pr oved the existence of finite coefficients in the Mayer activity expans ion up to order 2n below a series of temperature thresholds T-n = T-in finity[1 + (2n - 1)(-1)] (n = 1, 2,...). With this in mind they conjec tured that an infinite sequence of intermediate, multipole phases appe ars between the exponentially screened plasma phase above T-1 and the full, unscreened Kosterlitz-Thouless phase below T-infinity = T-KT. We demonstrate that Debye-Huckel-Bjerrum theory, as recently investigate d for d = 2 dimensions, provides a natural and quite probably correct explanation of the pattern of finite Mayer coefficients while indicati ng the total absence of any intermediate phases at nonzero density rho ; only the KT phase extends to rho > 0.