Journal of Statistical Physics, Vol. 39, 133--156, 1985

Authors: G. Gallavotti and F. Nicolo'

Title The "Screening Phase Transitions" in the Two-Dimensional Coulomb Gas :

Abstract: The Mayer series of a Coulomb gas with fixed ultraviolet cutoff is studied in two dimensions. In particular, we show the existence of infinitely many thresholds T n = (e2/8~k)(1- 1/2n) 1, k =Boltzmann's constant, e=electric charge, n = 1, 2,..., which are conjectured to reflect a sequence of transitions from pure mul- tipole phase (the Kosterlitz Thouless region) to a plasma phase (the Debye screening region) via an infinite number of "intermediate phases." Mathematically we prove that the Mayer series' coefficients of order up to 2n are finite if the temperature T is < T,,. For T< T~ all the coefficients are finite and the gas can he formally interpreted as a multipole gas with multipoles with finite activity.

Key words:  Coulomb gas; sine-Gordon field theory; renormalization group; multipole gas
Giovanni Gallavotti
Dipartimento di Fisica, INFN
Universita' di Roma "La Sapienza"
P.le A. Moro 2
I 00185 Roma, Italia