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

## TL;DR

This paper investigates the effects of elastic interactions on a Hubbard pair cluster, analyzing thermal expansion, magnetostriction, and electrostriction across various temperatures and external fields within an extended Hubbard model.

## Contribution

It introduces a comprehensive study of elastic interactions in a Hubbard dimer, deriving an equation of state and analyzing deformation effects under different conditions.

## Key findings

- Thermal expansion varies with temperature and external fields.
- Magnetostriction and electrostriction effects are characterized across parameter ranges.
- Deformation responses depend on the interplay of elastic and electronic interactions.

## Abstract

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.