Geometrically-Frustrated Pseudogap Phase of Coulomb Liquids

We study a class of models with long-range repulsive interactions of the generalized Coulomb form $V(r)\sim 1\mathrm{/}{r}^{\alpha }$. 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.