Nonextensive thermodynamics of the two - site Hubbard model . II . Grand - canonical ensembles

We have discussed thermodynamical and magnetic properties of the grand-canonical ensembles of the half-filled two-site Hubbard model within the framework of the nonextensive statistics (NES). For relating the physical temperature T to the Lagrange multiplier β, two methods have been adopted: T = 1/k B β in the method A [Tsallis et al. Physica A 261 (1998) 534], and T = c q /k B β in the method B [Abe et al. 126], where k B is the Boltzman constant and c q a sum of the escort probability. The temperature dependences of specific heat and magnetic susceptibility have been calculated for the entropic index q with 1 < = q < = 2, the conventional Boltzman-Gibbs statistics being recovered in the limit of q = 1. The Curie constant Γ q of the susceptibility in the atomic and low-temperature limits with t/U = T /U = 0 is shown to be given by Γ q = 2q2 2(q−1) in the method A, and Γ q = 2 q in the method B, where t stands for electron hoppings and U intra-atomic interaction in the Hubbard model. It has been shown that these expressions agree with the results of a free spin model which has been studied also by the NES with the methods A and B.