  We comment on zero- and low-temperature structural phase transitions,
expecting that these comments might be relevant not only for this structural
case. We first consider a textbook model whose classical version is the only
model for which the Landau theory of phase transitions and the concept of
``soft mode'' introduced by Ginzburg are exact. Within this model, we reveal
the effects of quantum fluctuations and thermal ones at low temperatures. To do
so, the knowledge of the dynamics of the model is needed. However, as already
was emphasized by Ginzburg et al. in eighties, a realistic theory for such a
dynamics at high temperatures is lacking, what also seems to be the case in the
low temperature regime. Consequently, some theoretical conclusions turn out to
be dependent on the assumptions on this dynamics. We illustrate this point with
the low-temperature phase diagram, and discuss some unexpected shortcomings of
the continuous medium approaches.
