We develop a field theoretical approach to the cold interstellar medium ( ISM ) .
We show that a non-relativistic self-gravitating gas in thermal equilibrium with variable number of atoms or fragments is exactly equivalent to a field theory of a single scalar field \phi ( { \vec { x } } ) with exponential self-interaction .
We analyze this field theory perturbatively and non-perturbatively through the renormalization group approach .
We show scaling behaviour ( critical ) for a continuous range of the temperature and of the other physical parameters .
We derive in this framework the scaling relation \Delta M ( R ) \sim R ^ { d _ { H } } for the mass on a region of size R , and \Delta v \sim R ^ { q } for the velocity dispersion where q = \frac { 1 } { 2 } ( d _ { H } -1 ) .
For the density-density correlations we find a power-law behaviour for large distances \sim| { \vec { r } _ { 1 } } - { \vec { r } _ { 2 } } | ^ { 2 d _ { H } -6 } .
The fractal dimension d _ { H } turns to be related with the critical exponent \nu of the correlation length by d _ { H } = 1 / \nu .
The renormalization group approach for a single component scalar field in three dimensions states that the long-distance critical behaviour is governed by the ( non-perturbative ) Ising fixed point .
The corresponding values of the scaling exponents are \nu = 0.631... , d _ { H } = 1.585... and q = 0.293... .
Mean field theory yields for the scaling exponents \nu = 1 / 2 , d _ { H } = 2 and q = 1 / 2 .
Both the Ising and the mean field values are compatible with the present ISM observational data : 1.4 \leq d _ { H } \leq 2 , 0.3 \leq q \leq 0.6 .

As typical in critical phenomena , the scaling behaviour and critical exponents of the ISM can be obtained without dwelling into the dynamical ( time-dependent ) behaviour .

The relevant rôle of selfgravity is stressed by the authors in a Letter to Nature , September 5 , 1996 .