  We make a short overview of the recent analytic and numerical studies of the
classical two-dimensional XY and Heisenberg models at low temperatures. Special
attention is being paid to an influence of finite system size L on the
peculiarities of the low-temperature phase. In accordance with the
Mermin-Wagner-Hohenberg theorem, spontaneous magnetisation does not appear in
the above models at infinite L. However it emerges for the finite system sizes
and leads to new features of the low-temperature behaviour.
