Duality-based approximation for the critical point of the square lattice Ising ferromagnet within Tsallis statistics

Within the generalized thermostatistics of Tsallis, we propose for the spin-12 Ising ferromagnet a transmissivity variable which extends that defined by Tsallis and Levy for thermal magnetic systems. By using this generalized transmissivity as well as duality arguments, we calculate the q-dependence of the critical temperature corresponding to the square lattice, where q is the entropic index (q = 1 reproduces standard thermostatistics). Our approximate results are compared with those previously obtained using renormalization group and mean-field approximation.