Nonextensive Thermodynamics of a Cluster Consisting of M Hubbard Dimers (M=1,2,3 and ∞)(COMPLEXITY AND NONEXTENSIVITY:NEW TRENDS IN STATISTICAL MECHANICS)

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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 nonex-tensive statistics (NES). We have calculated temperature and magnetic-field dependences of the specific heat and susceptibility for M=1, 2, 3 and ∞, assuming the relation between M and the entropic index q given by q=1+1/M, which was previously derived by several methods. For relating the physical temperature T to the Lagrange multiplier β, two methods have been adopted: T=1/k_Bβ in the method A [C. Tsallis et al., Physica A 261 (1998), 534], and T= c_q/k_Bβ in the method B [S. Abe et al., Phys. Lett. A 281 (2001), 126], where k_B denotes the Boltzman constant, c_q=Σ_iP^q_i, and p_i the probability distribution of the ith state. A comparison between the results calculated by the two methods suggests that the method B may be more appropriate than the method A for small-scale systems.
2006-06-05