  Topological phase space disconnection has been recently found to be a general
phenomenon in isolated anisotropic spin systems. It sets a general framework to
understand the emergence of ferromagnetism in finite magnetic systems starting
from microscopic models without phenomenological on-site barriers. Here we
study its relevance for finite systems with long range interacting potential in
contact with a thermal bath. We show that, even in this case, the induced
magnetic reversal time is exponentially large in the number of spins, thus
determining {\it stable} (to any experimental observation time) ferromagnetic
behavior. Moreover, the explicit temperature dependence of the magnetic
reversal time obtained from the microcanonical results, is found to be in good
agreement with numerical simulations. Also, a simple and suggestive expression,
indicating the Topological Energy Threshold at which the disconnection occurs,
as a real energy barrier for many body systems, is obtained analytically for
low temperature.
