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arXiv:1808.04310 · Physica A Statistical Mechanics and its Applications

Hubbard pair cluster in the external fields. Studies of the polarization and susceptibility

T. Balcerzak, Karol Szałowski

Published Aug 16, 2018• 11 citations
arXivHTMLPDF
DOI
10.1016/j.physa.2018.08.152

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The thermodynamic and correlation functions for one- and three- dimensional systems described by the half-filled band Hubbard Hamiltonians are evaluated in the pair-approximation of cluster variation method. The energy, specific heat, magnetization, susceptibility and various equilibrium correlation functions are computed as functions of temperature as well as the external magnetic field for different values of coulomb energies. Our solutions correspond to Bethe approximation in which the relevant pair-correlation functions are included in our formulation. It is observed that the chemical potential for the half-filled band is exactly half of the coulomb energy at all temperatures, irrespective of the value of the applied magnetic field.
The Hubbard model for small size clusters is investigated.Using direct diagonalization of the small cluster Hamiltonian, electronic, magnetic and spin susceptibilities are calculated and their behavior at low temperature is investigated.The temperature behavior of susceptibilities for twoand three-site clusters is investigated for both center and edge of the Brillouin zone.If at the given concentration the ground state is polarized, the susceptibilities diverge following the Curie law and the system is transformed into the magnetically ordered state at T = 0.