  We study, for $SU(2)$ Yang-Mills theories discretized on a lattice, a
non-local topological order parameter, the center flux ${{z}}$. We show that:
i) well defined topological sectors classified by $\pi_1(SO(3))=\mathbb{Z}_2$
can only exist in the ordered phase of ${{z}}$; ii) depending on the dimension
$2 \leq d\leq 4$ and action chosen, the center flux exhibits a critical
behaviour sharing striking features with the Kosterlitz-Thouless type of
transitions, although belonging to a novel universality class; iii) such
critical behaviour does not depend on the temperature $T$. Yang-Mills theories
can thus exist in two different continuum phases, characterized by an either
topologically ordered or disordered vacuum; this reminds of a quantum phase
transition, albeit controlled by the choice of symmetries and not by a physical
parameter.
