  Starting from general considerations concerning phase transitions and the
many-body problem, a pedagogical introduction to the Mermin-Wagner theorem is
given. Particular attention is paid to how the Mermin-Wagner theorem fits in
with more general methods in many-particle physics. An attempt at an assessment
of its validity for approximative methods is made by contrasting the results
obtained within Onsager reaction-field theory and those obtained by the
well-known Tyablikov method.
