  We study properties of SU(2) Yang-Mills theory on a four-dimensional
Euclidean spacetime in which two directions are compactified into a finite
two-dimensional torus ${\mathbb T}^2$ while two others constitute a large
${\mathbb R}^2$ subspace. This Euclidean ${\mathbb T}^2 \times {\mathbb R}^2$
manifold corresponds simultaneously to two systems in a (3+1) dimensional
Minkowski spacetime: a zero-temperature theory with two compactified spatial
dimensions and a finite-temperature theory with one compactified spatial
dimension. Using numerical lattice simulations we show that the model exhibits
two phase transitions related to the breaking of center symmetries along the
compactified directions. We find that at zero temperature the transition lines
cross each other and form the Greek letter $\gamma$ in the phase space
parametrized by the lengths of two compactified spatial dimensions. There are
four different phases. We also demonstrate that the compactification of only
one spatial dimension enhances the confinement property and, consequently,
increases the critical deconfinement temperature.
