**Authors**:
G. Gallavotti and F. Nicolo'

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

email giovanni.gallavotti@roma1.infn.it