ISING-MODEL WITH 2-SPIN, 3-SPIN AND 4-SPIN INTERACTIONS

The two-state Ising model with nearest-neighbour bilinear exchange constant J(2), three-spin coupling constant J(3) and four-spin coupling constant J(4) is studied using the effective-field approximation. The temperature variation in spontaneous magnetization is studied for different coordination numbers z and for various values of the parameters alpha = J(3)/J(2) and alpha' = J(4)/J(2). It is seen that, in the absence of three-spin coupling, there exists a critical value of alpha' (say, alpha(c)') above which the magnetization becomes double valued at and beyond the Curie temperature T(C), forming a bulge near T(C) which indicates the occurrence of a first-order transition. The expressions for alpha(c)' for z = 3, 4, 6 are derived and it is found that alpha(c)' increases as z increases. In the absence of four-spin coupling it is found that first-order transitions appear for alpha greater-than-or-equal-to 0. The magnetization curves are also studied for the case when all the interactions are present. The results are discussed with reference to those obtained from the molecular-field approximation.