One-dimensional (1D) magnets show novel phenomena that originate from
quantum effects. In some of the 1D antiferromagnets the ground state i
s a singlet and there is an energy gap to the excited state. These inc
lude an antiferromagnet with a spontaneously dimerized state originati
ng from a competing interaction, and spin-Peierls materials. When a sp
in-Peierls system is doped with impurities, a long-range antiferromagn
etic ordering appears. Spin ladders show quite different magnetic prop
erties depending on the number of legs. When holes are introduced in a
ladder, they can be superconductive.