Abstract: Based on the transverse field Ising model，the phase transition properties of

square lattice nanois- lands with a spin of 1 /2 are investigated using the usual decoupling

approximation and higher order decoupling ap- proximation of the Fermi green function. The

polarization diagram shows that when the initial spin orientation is ran- dom，multiple and pseudo

solutions may be produced，thus show unconventional results: reentry phenomenon. The

use of high-order decoupling approximation can not only explain the richer phase transition

phenomenon，but also in most cases，the higher-order decoupling approximate equations have only a unique solution，which

can avoid the generation of pseudo solutions. JS / J is the main reason for the stepped shape of

the polarization curve，but the high order decoupling approximately increases the relationship between the parameters.

Key words: nanoisland, green's function, transverse field Ising model, pseudo-solution