  The ferromagnetic transition in the Ising model is the paradigmatic example
of ergodicity breaking accompanied by symmetry breaking. It is routinely
assumed that the thermodynamic limit is taken with free or periodic boundary
conditions. More exotic symmetry-preserving boundary conditions, like
cylindrical antiperiodic, are less frequently used for special tasks, such as
the study of phase coexistence or the roughening of an interface. Here we show,
instead, that when the thermodynamic limit is taken with these boundary
conditions, a novel type of transition takes place below $T_c$ (the usual Ising
transition temperature) without breaking neither ergodicity nor symmetry. Then,
the low temperature phase is characterized by a regime (condensation) of strong
magnetization's fluctuations which replaces the usual ferromagnetic ordering.
This is due to critical correlations perduring for all T below Tc. The argument
is developed exactly in the $d=1$ case and numerically in the d=2 case.
