Abstract :
In this paper I discuss a mechanism for ferrimagnetism in 1+1 dimensions. The mechanism is related to a special class of interactions described by operators with non-zero Lorentz spin. Such operators are present in such problems as the problem of tunneling between Luttinger liquids and the problem of frustrated spin ladder. Exact solutions are presented for a representative class of models possessing a continuous isotopic symmetry. It is shown that the interactions (i) dynamically generate static oscillations with the wave vector dependent on the coupling constant, (ii) give rise to spontaneous breaking of this symmetry at T=0 accompanied by generation of the magnetic moment and appearance of gapless modes with a non-relativistic (ferromagnetic) dispersion E∼k2, (iii) generate massive (roton) modes.
