  We study quantum ferrimagnets in one, two, and three dimensions by using a
variety of methods and approximations. These include: (i) a treatment based on
the spin coherent state path-integral formulation of quantum ferrimagnets by
taking into account the leading order quantum and thermal fluctuations (ii) a
field-theoretical (non-linear $\sigma$-model type) formulation of the special
case of one-dimensional quantum ferrimagnets at zero temperature (iii) an
effective description in terms of dimers and quantum rotors, and (iv) a quantum
renormalization group study of ferrimagnetic Heisenberg chains. Some of the
formalism discussed here can be used for a unified treatment of both
ferromagnets and antiferromagnets in the semiclassical limit. We show that the
low (high) energy effective Hamiltonian of a (S_1, S_2) Heisenberg ferrimagnet
is a ferromagnetic (antiferromagnetic) Heisenberg model. We also study the
phase diagram of quantum ferrimagnets in the presence of an external magnetic
field h ($h_{c1} < h < h_{c2}$) and show that the low- and the high-field
phases correspond respectively to the classical N\'eel and the fully polarized
ferromagnetic states. We also calculate the transition temperature for the
Berezinskii-Kosterlitz-Thouless phase transition in the special case of
two-dimensional quantum ferrimagnets.

Condensed Matter