For a model of interacting quantum particles of mass m oscillating in a double-well crystalline field, a mechanism of its stabilization by quantum effects is described. In particular, a stability condition involving m, the interaction intensity, and the parameters of the crystalline field is given. It is independent of the temperature and is satisfied if m is small enough and/or the tunneling frequency is big enough. It is shown that under this condition the infinite-volume free energy density is an analytic function of the external field and the displacement-displacement correlation function decays exponentially; hence, no phase transitions can arise at all temperatures. This gives a complete and rigorous answer to the question about the influence of quantum effects on structural phase transitions, the discussion of which was initiated in [T. Schneider, H. Beck, and E. Stoll, Phys. Rev. B 13, 1123 (1976)]].
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