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. •Hubbard model for a dimer (pair cluster) with elastic interactions and vibrational contribution is discussed.•Exact diagonalization method is applied within grand canonical ensemble approach.•External electric and magnetic field are taken into account.•The deformation of the dimer size under the influence of the temperature and fields is investigated.•Magnetostriction and electrostriction phenomena are extensively discussed.