Monte Carlo simulation of magnetic systems in the Tsallis statistics

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, in the thermodynamical limit, phase transitions at finite temperatures except for the extensive case q=1.