  Lttice-spin phonons are considered, which make the heat capacity at the
critical temperature satisfy experimental observations better. There is a BEC
phase transition in an Ising model attributable to the lattice-spin phonons. We
proved that the spin-wave theory only is available after BEC transition, and
the magnons have the same characteristics as the lattice-spin phonons',
resulting from quantum effect. Energy-level overlap effect at ultralow
temperature is found. A prediction of BEC phase transition in a crystal is put
forward as our theory generalization.
