  This article consider a situation of SU(N) system with broken symmetry, and
therefore the spin-liquid phase is exist in the phase transition stage. And
explore the antiferromagnetic spin interaction with long range order in a two
dimension square lattice using the two alkaline earth atoms state short range
interaction. The appearance of spin liquid due to noncolline mechanism which
causing by destruction of long range order in this model is mentioned. In a
N-site fermion-model system, I analyse the effect of fluctuation on order and
phase transition. As well as this N-component spin system with disordered spin,
the critical phenomenon is showed to reflect the fluctuation effection on
process of phase transtion.
