We construct and analyze a frustrated quantum spin model with plaquette ord
er, in which the low-energy dynamics is controlled by spin singlets. At a c
ritical value of frustration the singlet spectrum becomes gapless, indicati
ng a quantum transition to a phase with dimer order. The magnetic susceptib
ility has an activated form throughout the phase diagram, whereas the speci
fic heat exhibits a rich structure and a power-law dependence on temperatur
e at the quantum critical point. This generic behavior can be relevant to q
uantum antiferromagnets on Kagome and pyrochlore lattices where (almost) al
l low-energy excitations are spin singlets, as well as to the CaV4O9 lattic
e and the strongly frustrated antiferromagnets Cu2Te2O5(Cl,Br)(2) and Li2VO
(Si,Ge)O-4.