  We apply the Broad Histogram Method to an Ising system in the context of the
recently reformulated Generalized Thermostatistics, and we claim it to be a
very efficient simulation tool for this non-extensive statistics. Results are
obtained for the nearest-neighbour version of the Ising model for a range of
values of the $q$ parameter of Generalized Thermostatistics. We found an
evidence that the 2D-Ising model does not undergo phase transitions at finite
temperatures except for the extensive case $q=1$.
