The staggered charge-order phase of the extended Hubbard model in the atomic limit

We study the phase diagram of the extended Hubbard model in the atomic limit. At zero temperature, the phase diagram decomposes into six regions: three with homogeneous phases (characterized by particle densities rho = 0, 1 and 2 and staggered charge density Delta = 0) and three with staggered phases (characterized by the densities rho = 1/2, 1 and 3/2 and staggered densities \Delta\ = 1/2, 1, and 1). Here we use Pirogov-Sinai theory to analyse the details of the phase diagram of this model at low temperatures. In particular, we show that for any sufficiently low non-zero temperature the three staggered regions merge into one staggered region S, without any phase transitions (analytic free energy and staggered order parameter Delta) within S.