  We study a class of models with long-range repulsive interactions of the
generalized Coulomb form $V(r)\sim 1/r^{\alpha}$. We show that decreasing the
interaction exponent in the regime $\alpha < d$ dramatically depresses the
charge ordering temperature $T_c$ in any dimension $d\ge 2$, reflecting the
strong geometric frustration produced by long-range interactions. A nearly
frozen Coulomb liquid then survives in a broad pseudogap phase found at $T >
T_c$, which is characterized by an unusual temperature dependence of all
quantities. In contrast, the leading critical behavior very close to the
charge-ordering temperature remains identical as in models with short-range
interactions.
