Tricritical point in charge-order systems and its criticality are studied for a microscopic model by using the mean-field approximation and exchange Monte Carlo method in the classical limit as well as by using the Hartree-Fock approximation for the quantum model. We study the extended Hubbard model and show that the tricritical point emerges as an endpoint of the first-order transition line between the disordered phase and the charge-ordered phase at finite temperatures. Strong divergences of several fluctuations at zero wavenumber are found and analyzed around the tricritical point. Especially, the charge susceptibility χc and the susceptibility of the next-nearest-neighbor correlation χR are shown to diverge and their critical exponents are derived to be the same as the criticality of the susceptibility of the double occupancy χD(0). The singularity of conductivity at the tricritical point is clarified. We show that the singularity of the conductivity σ is governed by that of the carrier density and is given as |σ - σc| ∼ |g - gc|pt (A log |g - gc| + B), where g is the effective interaction of the Hubbard model, σc (gc) represents the critical conductivity(interaction) and A and B are constants, respectively. Here, in the canonical ensemble, we obtain pt = 2βt = 1/2 at the tricritical point. We also show that pt changes into p′t = 2β = 1 at the tricritical point in the grand-canonical ensemble when the tricritical point in the canonical ensemble is involved within the phase separation region. The results are compared with available experimental results of organic conductor (DI-DCNQI)2Ag.
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