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In this work we present a thorough analysis of the phase transitions thatoccur in a ferromagnetic 2D Ising model, with only nearest-neighborsinteractions, in the framework of the Tsallis nonextensive statistics. Weperformed Monte Carlo simulations on square lattices with linear sizes Lranging from 32 up to 512. The statistical weight of the Metropolis algorithmwas changed according to the nonextensive statistics. Discontinuities in them(T) curve are observed for $q\leq 0.5$. However, we have verified only onepeak on the energy histograms at the critical temperatures, indicating theoccurrence of continuous phase transitions. For the $0.5<q\leq 1.0$ regime, wehave found continuous phase transitions between the ordered and the disorderedphases, and determined the critical exponents via finite-size scaling. Weverified that the critical exponents $\alpha $, $\beta $ and $\gamma $ dependon the entropic index $q$ in the range $0.5<q\leq 1.0$ in the form $\alpha(q)=(10 q^{2}-33 q+23)/20$, $\beta (q)=(2 q-1)/8$ and $\gamma(q)=(q^{2}-q+7)/4$. On the other hand, the critical exponent $\nu $ does notdepend on $q$. This suggests a violation of the scaling relations $2 \beta+\gamma =d \nu $ and $\alpha +2 \beta +\gamma =2$ and a nonuniversality of thecritical exponents along the ferro-paramagnetic frontier.

Finite size analysis of a two-dimensional Ising model within a nonextensive approach