Hubbard pair cluster with elastic interactions. Studies of thermal expansion, magnetostriction and electrostriction

The pair cluster (dimer) is studied within the framework of the extended Hubbard model and the grand canonical ensemble. The elastic interatomic interactions and thermal vibrational energy of the atoms are taken into account. The total grand potential is constructed, from which the equation of state is derived. In equilibrium state, the deformation of cluster size, as well as its derivatives, are studied as a function of the temperature and the external magnetic and electric fields. In particular, the thermal expansion, magnetostriction and electrostriction effects are examined for arbitrary temperature, in a wide range of Hamiltonian parameters.