We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a large number of degrees of freedom, and both short- and...

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.