Phase diagrams of the spin-1/2 ising system on two dimensional lattices

ABSTRACT In this work, we have studied the Kaneyoshi's differential operator technique in spin-1/2 Ising systems, i. e., the effective field theory ( EFT ) with correlations on honeycomb, square and triangular lattices in which attention is focused on a cluster comprising a central spin, labeled 0, and the z nearest-neighbor spins with which it directly interacts. With the use of differential operator technique and Ising spin identity, a new simple method is developed, by deriving a set of linear equations for the spin-1/2 Ising systems with three coordination numbers z (z = 3,4, 6) at calculating without the decoupling approximation of the canonical ensemble averages < si >,< SiSj >,< SiSjSk > and < SiSj...sz >. By solving numerically the set of linear equations derived individually for the Ising systems, we have obtained the one, two and higher spin correlation functions as a function of temperature. The anti-Curie point has not been observed in our systems. Furthermore we have determined the phase diagrams of the spin-1/2 transverse Ising systems plotted in the (-y-,7) space. The obtained critical values of ^j and 7 are in good agreement with the theoretical studies in the literature.