  Effects of geometrical frustration and quantum fluctuation are theoretically
investigated for the proton ordering in a quasi-two-dimensional hydrogen-bonded
system, squaric acid crystal. We elucidate the phase diagram for an effective
model, the transverse-field Ising model on a frustrated checkerboard lattice,
by using quantum Monte Carlo simulation. A crossover to liquidlike paraelectric
state with well-developed molecular polarizations is identified,
distinguishably from long-range ordering. Emergence of long-range order from
the liquidlike state exhibits peculiar aspects originating from the lifting of
quasi-macroscopic degeneracy, such as colossal enhancement of the transition
temperature and a vanishingly small anomaly in the specific heat.
