  In frustrated magnetic systems with competing interactions fluctuations can
lift the residual accidental degeneracy. We argue that the state selection may
have different outcomes for quantum and thermal order by disorder. As an
example, we consider the semiclassical Heisenberg fcc antiferromagnet with only
the nearest-neighbor interactions. Zero-point oscillations select the type 3
collinear antiferromagnetic state at T=0. Thermal fluctuations favor instead
the type 1 antiferromagnetic structure. The opposite tendencies result in a
finite-temperature transition between the two collinear states. Competition
between effects of quantum and thermal order by disorder is a general
phenomenon and is also realized in the J1-J2 square-lattice antiferromagnet at
the critical point J2 = 0.5 J1.
