The semi-infinite anisotropic spin-1/2 Heisenberg ferromagnet

Using the effective field theory with a probability distribution technique that accounts for the self-spin correlation functions, the phase transition s in the semi-infinite anisotropic spin-1/2 Heisenberg ferromagnet on a sim ple cubic lattice are examined. For fixed values of the reduced exchange an isotropic parameter, the critical temperature of the system is studied as a function of the ratio R of the surface exchange couplings to the bulk ones . It was found that if R less than or equal to R-c, the system orders at th e bulk critical temperature T-c(B)/J and if R greater than or equal to R-c, the system exhibits two successive transitions. The surface orders at the surface critical temperature T-c(S)/J which is higher than T-c(B)/J and as the temperature is lowered, in the presence of an ordered surface, the bulk orders at T-c(B)/J.