Ising model in the Rényi statistics: the finite size effects

The Rényi statistics is applied for a description of finite size effects in the 1D Ising model. We calculate the internal energy of the spin chain and the system temperature using the Rényi distribution and postulate them to be equal to their counterparts, obtained in the microcanonical ensemble. It allows us to self-consistently derive the Rényi $q$-index and the Lagrange parameter $T$ to relate them to the physically observed system temperature $T_{\mathrm{p}\mathrm{h}}$, and to show that the entropic phase transitions are possible in a broad temperature domain. We have also studied the temperature dependence of the internal energy $U(T_{\mathrm{p}\mathrm{h}})$ at constant $q$ and an influence of the size related effects on the system thermodynamics.