Investigating global phase diagrams (GPDs) with reentrant transition behavior

In this paper we calculate the global phase diagrams with the closed-loop behavior for the phase transition of physical systems by means of the transverse field Ising model with nearest neighbor interaction. The 3D graph plotted by the various physical parameters gives a clear appreciation and qualitative understanding of the reentrant phase behavior of the system. Meanwhile the results show the close correlation between experimental phenomena and our theoretical calculation for the closed-loop behavior for the phase transition of the systems.