  Monte Carlo simulations of the magnetization temperature dependence in
$D\times L$ nanotubes (periodic lateral boundary conditions) and nanostrips
(free lateral boundary conditions) with $D$=8, 16, 32, 64$\ll L\longrightarrow
5000$ have been performed. The apparent critical temperature was determinated
using the Binder Cumulant method (crossing of data for $D\times L$ with data
for $D\times 2L)$ and it was found to be $ T_{C}=0 $ for small $D$ values
$(D<D^{\ast})$, as it might have been expected.
