  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 chi_c and the susceptibility of the next-nearest-neighbor
correlation chi_R are shown to diverge and their critical exponents are derived
to be the same as the criticality of the susceptibility of the double occupancy
chi_D0. The singularity of conductivity at the tricritical point is clarified.
We show that the singularity of the conductivity sigma is governed by that of
the carrier density and is given as
|sigma-sigma_c|=|g-g_c|^{p_t}Alog{|g-g_{c}|}+B), where g is the effective
interaction of the Hubbard model, sigma_c g_c represents the critical
conductivity(interaction) and A and B are constants, respectively. Here, in the
canonical ensemble, we obtain p_t=2beta_t=1/2 at the tricritical point. We also
show that p_t changes into p_{t}'=2beta=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.
