Most of low dimensional lattice magnets undergo magnetic transitions into long range ordered phases due to extra interactions in addition to the ordinal nearest neighbor exchange interaction. The competition among these interactions gives rise to a variety of magnetic phases having incommensurate structure and partially disordered structure. These structures appear in the transition scheme of successive phase transition including fast order transition. The transiton belongs to a new universality class in some cases. External magnetic field also gives remarkable changes in the magnetic structure. Low dimensionality of the lattice favors quantum effect such as Haldane gap.
