**Author**: J. G.
Gallavotti, T.F. Lin

**Title**: *
One dimensional lattice gases with rapidly decreasing
interactions
*

**Abstract:**
We consider the pressure and the correlation functions of a one
dimensional lattice gas in which the mutual interaction decreases as
$r \exp(-n^t)$, ($r,t>0$), when the nterparticle distance
$n\to\infty$. We prove that such a system cannot show phase
transitions of order $k\ge1$ in the sense that the pressure and the
corelation functions are infinitely differentiable with respect to any
relevant parameter (such as th temperature or the chemical potential).

**Key words: **Equilibrium
Statistical Mechanics, Absence Phase Transitions, Gibbs States,

Giovanni Gallavotti

Fisica, Universita' di Roma 1

P.le Moro 2

00185 Roma, Italia

tel +39-06-4991-4370

fax +39-06-4957697

em giovanni.gallavotti@roma1.infn.it

http://ipparco.roma1.infn.it