Suppression of critical fluctuations by strong quantum effects in quantum lattice systems

Translation invariant models of quantum anharmonic oscillators with a polynomial anharmonicity and a ferroelectric interaction are considered. For these models, it is proved that the critical fluctuations of the position operator, peculiar to the critical point, are suppressed at all temperatures provided the oscillators are strongly quantum, This phenomenon is shown to occur in particular if the oscillator's mass is less than some threshold value depending on the anharmonicity parameters.