nd - m at . s ta t - m ec h ] 1 1 Ja n 20 05 1 Nonextensive thermodynamics of a cluster consisting of M Hubbard dimers ( M = 1 , 2 , 3 and ∞

The thermodynamical property of a small cluster including M Hubbard dimers, each of which is described by the two-site Hubbard model, has been discussed within the nonextensive statistics (NES). We have calculated the temperature dependence of the energy, entropy, specific heat and susceptibility for M = 1, 2, 3 and ∞ (corresponding to q = 1), assuming the relation between the entropic index q and the cluster size N given by q = 1 + 2/N (N = 2 M for M dimers), which was previously derived by several methods. We have pointed out that although the joint probability of a system consisting of independent subsystems (e.g. dimers) is conventionally expressed a priori as the product of the probabilities of constituent elements, it is not necessarily the case in the NES, which is supported by our model calculations. The susceptibility and specific heat of spin dimers described by the Heisenberg model have been discussed also by using the NES.