  We consider the massive vector $N$-component $(\lambda\varphi^{4})_{D}$
theory defined on a Euclidean space with a toroidal topology. Using recently
developed methods to perform a compactification of a $d$-dimensional subspace
at finite chemical potential, we treat jointly the effects of temperature and
spatial boundaries, setting forth grounds for an analysis of spontaneous
symmetry restoration driven by temperature and spatial boundaries as a function
of the chemical potential. We restrict ourselves to d=2, which corresponds to
the heated system confined between two parallel planes (separation $L$) in
dimensions D=3 and D=4. We present results, in the large-$N$ limit, which
exhibit how finite size and chemical potential affect spontaneous symmetry
restoration.
