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In our earlier work [M. Hafez, et al., Phys. Lett. A 373 (2009) 4479] we employed the flow equation method
to obtain a classical effective model from a quantum mechanical parent Hamiltonian called, the ionic Hubbard
model (IHM). The classical ionic Hubbard model (CIHM) obtained in this way contains solely Fermionic occupation
numbers of two species corresponding to particles with $\uparrow $and$ \downarrow$ spin, respectively. In this paper, we employ the transfer matrix method to analytically solve the CIHM at finite temperature in one dimension. In
the limit of zero temperature, we find two insulating phases at large and small Coulomb interaction strength, U,
mediated with a gap-less metallic phase, resulting in two continuous metal-insulator transitions. Our results are
further supported with Monte Carlo simulations.
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