  A mechanism for ferrimagnetism in
  (1+1)-dimensions is discussed. The ferrimagnetism is cased by interactions
described by operators with non-zero conformal spin. Such interactions appear
in such problems as the problem of tunneling between Luttinger liquids and the
problem of frustrated spin ladder. I present exact solutions for a
representative class of models containing such interactions together with a
simple mean field analysis. It is shown that the interactions (i) dynamically
generate static oscillations with a wave vector dependent on the coupling
constant, (ii) give rise to a finite magnetic moment at $T = 0$ accompanied by
the soft mode with a non-relativistic ({\it ferromagnetic}) dispersion $E \sim
k^2$, (iii) generate massive (roton) modes.
