  The out-of-time-order correlators (OTOCs) is used to study the quantum phase
transitions (QPTs) between the normal phase and the superradiant phase in the
Rabi and few-body Dicke models with large frequency ratio of theatomic level
splitting to the single-mode electromagnetic radiation field frequency. The
focus is on the OTOC thermally averaged with infinite temperature, which is an
experimentally feasible quantity. It is shown that thecritical points can be
identified by long-time averaging of the OTOC via observing its local minimum
behavior. More importantly, the scaling laws of the OTOC for QPTs are revealed
by studying the experimentally accessible conditions with finite frequency
ratio and finite number of atoms in the studied models. The critical exponents
extracted from the scaling laws of OTOC indicate that the QPTs in the Rabi and
Dicke models belong to the same universality class.
