  We explore the dependence of vacuum energy on the boundary conditions for
massive scalar fields in (2 + 1)-dimensional spacetimes. We consider the
simplest geometrical setup given by a two-dimensional space bounded by two
homogeneous parallel wires in order to compare it with the non-perturbative
behaviour of the Casimir energy for non-Abelian gauge theories in (2 + 1)
dimensions. Our results show the existence of two types of boundary conditions
which give rise to two different asymptotic exponential decay regimes of the
Casimir energy at large distances. The two families are distinguished by the
feature that the boundary conditions involve or not interrelations between the
behaviour of the fields at the two boundaries. Non-perturbative numerical
simulations and analytical arguments show such an exponential decay for
Dirichlet boundary conditions of SU(2) gauge theories. The verification that
this behaviour is modified for other types of boundary conditions requires
further numerical work. Subdominant corrections in the low-temperature regime
are very relevant for numerical simulations, and they are also analysed in this
paper.
