The hadron multiplicity distributions and factorial moments are studie
d in the framework of Landau theory of phase transitions. The factoria
l moments show a scaling law with a scaling exponent nu which characte
rizes the intermittency properties of the hadron phase for T<T-c (or T
-t) where T-c (or T-t) is the transition temperature for second (or fi
rst) order transition. The scaling exponent nu is weakly dependent on
the free energy parameters as well as on temperature. It is shown that
nu remains practically constant in the hadron phase for which T<T-c o
r T<T-t whether the transition is second order or first order of secon
d kind where the free energy expansion includes cubic term. This unive
rsality in the scaling exponent is also maintained above T-c over a wi
de range of temperature even if the transition is strongly first order
of first kind where the free energy expansion has only even order coe
fficients, except around the critical temperature T-t where T-t>T-c. T
herefore, the scaling exponent nu is rather more universal and only in
dicates the presence of a possible phase transition. It is further sho
wn that the hadron multiplicity distribution is quite sensitive to the
free energy parameters. The study of hadron multiplicity distribution
at various resolution or bin size reveals more information about the
dynamics of the phase transition. The calculated hadron multiplicity d
istributions are also compared with the negative binomial distribution
, often used to explain the experimental multiplicity distributions.