Abstract

The ferromagnetic Heisenberg model on the finite most symmetrical Cayley tree is studied in the limit of large size. The spectrum and wavefunctions of the single-magnon states are obtained rigorously. They have many unusual properties. The magnon.density excited as a whole at infinitesimal temperatures is logarithmically divergent when the mag-non is approximated as boson. Nevertheless, the possibility of some spontaneous magnetiza-tion at the central part of the tree remains.