We present a new method devised to overcome the intrinsic difficulties associated to the numerical simulations of the Tsallis statistics. We use a standard Metropolis Monte Carlo algorithm at a fictitious temperature T′, combined with a numerical integration method for the calculation of the...

We compute the internal energy of different Ising-type models, both long and short range, under Tsallis statistics using the microcanonical and the canonical ensemble and we discuss under which conditions both ensembles give equivalent results.