  It is argued that, using the black hole area entropy law together with the
Boltzmann-Gibbs statistical mechanics and the quasinormal modes of the black
holes, it is possible to determine univocally the lowest possible value for the
spin $j$ in the context of the Loop Quantum Gravity theory which is
$j_{min}=1$. Consequently, the value of Immirzi parameter is given by $\gamma =
\ln 3/(2\pi\sqrt{2})$. In this paper, we have shown that if we use Tsallis
microcanonical entropy rather than Boltzmann-Gibbs framework then the minimum
value of the label $j$ depends on the nonextensive $q$-parameter and may have
values other than $j_{min}=1$.
