  We propose an effective theory for the critical phase of a quantum
ferrimagnetic chain with alternating spins 1 and 1/2 in an external magnetic
field. With the help of the matrix product variational approach, the system is
mapped to a spin-1/2 XXZ chain in an (effective) magnetic field; as a
byproduct, we obtain an excellent description of the optical magnon branch in
the gapped phase. Recent finite-temperature DMRG results for the
low-temperature part of the specific heat are well described by the present
approach, and the ``pop-up'' peaks, developing near the critical field values
and in the middle of the critical phase, are identified with the contributions
from two different spinon bands of the effective spin-1/2 chain. The effect
should be as well observable in other spin-gap systems in an external field,
particularly in spin ladders.
