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\begin{document}
\title{Some exact results for the extended Hubbard model with intersite charge and magnetic interactions at atomic limit}
\author{\underline{Konrad~Kapcia}}
\affiliation{Faculty of Physics, Adam Mickiewicz University in Pozna\'n, Umultowska 85, 61-614 Pozna\'n, Poland}
\author{Waldemar~K\l{}obus}
\affiliation{Faculty of Physics, Adam Mickiewicz University in Pozna\'n, Umultowska 85, 61-614 Pozna\'n, Poland}
\author{Stanis\l{}aw~Robaszkiewicz}
\affiliation{Faculty of Physics, Adam Mickiewicz University in Pozna\'n, Umultowska 85, 61-614 Pozna\'n, Poland}
\begin{abstract}
The extended Hubbard model in the zero-bandwidth limit is studied.
The effective Hamiltonian consists of (i)~the on-site interaction $U$, (ii)~the intersite density-density interaction $W$ and (iii)~the intersite Ising-like magnetic exchange interaction $J$ between nearest-neighbors [1,2].
We present rigorous results obtained within the transfer-matrix method for one dimensional chain in two particular cases: (a)~\mbox{$W=0$} and \mbox{$n=1$} (\mbox{$U$-$J$} model); (b)~\mbox{$U\rightarrow+\infty$} and \mbox{$n=1/2$} (\mbox{$W\neq 0$}, \mbox{$J\neq 0$}). We obtain the exact formulas for the partition function and free energy what enable to calculate the thermodynamic properties such as entropy $S$,  specific heat $C$ and double occupancy per site $D$.


\textbf{References:}
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{\scriptsize[1] K.~Kapcia, W. K\l{}obus, and S.~Robaszkiewicz, \textit{Acta. Phys. Pol.}~A \textbf{121}, 1032 (2012).}

{\scriptsize[2] F. Mancini, E. Plekhanov, and G. Sica, J. Phys.: Conf. Series \textbf{391}, 012148 (2012).}
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\textit{The work has been financed by NCN as a project No. DEC-2011/01/N/ST3/00413 and as the doctoral scholarship No. DEC-2013/08/T/ST3/00012 as well as by ESF--OP Human Capital--POKL.04.01.01-00-133/09-00.}
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