Phase Diagrams for Generalized Spin Ising Model by using Linear Chain Approximation and Monte Carlo Simulations

The general Spin-sigma Ising Model has been studied using Linear Chain Approximation (LCA) and Monte Carlo (MC) Simulations. Phase diagrams in reduced anisotropy as a function of reduced temperature plane were obtained, for special case of sigma = 1 and 2, are qualitatively the same as those of the usual Mean Field Theory and Pair Approximation based on Bogoliubov inequality for the free energy. For the case sigma = 1 and low temperatures there is a first- line and one second-order line, which are connected to special point so called tricritical point (TCP). For sigma = 3/2, tricritical phenomena there is not, but there exists a first-order line separating phases m(1) = 3/2 and m(2) = 1/2 which ends at an isolated multiphase critical point. At the last, the phase diagrams for sigma = 2 are similar to those for sigma = 1, but the main difference is the existence of an additional ferromagnetic phase at low temperatures. For this case, the phase diagram shows reentrance transition lines behavior but could be an artifact of the present method. MC simulations were done on simple cubic lattices and in below cases are obtained general trend of the mean field like approach. Only for case sigma = 3/2 the present results are very different with MF theory where the first-line transition does not terminate on the second-order transition line. In sum, it was shown that the phase diagram for the generalized Ising model does not depend on the method but is intrinsic to the model.