The spin-3/2 Blume–Capel model with competing short- and long-range interactions

Abstract

Abstract The phase diagrams of the spin- 3 / 2 Blume–Capel model with competing short and long-range interactions were studied through the free energy density obtained by analytical methods. The competition emerges when positive short-range interactions of strength K arranged in a linear chain tend to establish an anti-parallel spin order, whereas negative long-range interactions − J tend to align them in parallel. Thus, no ferromagnetic order exists for K / J > 0.25 . So, the phase-diagrams were scanned by varying the values of K , for 0 K / J 0.25 . As in other similar study done for the spin-1 case, the second-order frontier separating the ferromagnetic and the paramagnetic phases is transformed gradually into a first-order line when K / J is greater than a certain critical value. Accordingly, there is a sub interval of K , for which two tricritical points appear restricting the length of the second-order frontier. Nevertheless, for greater values of K / J , the ferromagnetic–paramagnetic frontier becomes wholly of first order. Also, the typical line of coexistence of the spin- 3 / 2 Blume–Capel model, which divides two different ferromagnetic phases of magnetization m = 3 / 2 and m = 1 / 2 , becomes more complex by giving rise to another first-order line with a reentrant behavior that encloses a third ordered phase. In this case, the competition is such that there is a region in the phase diagram, where for each spin i with S i = 3 / 2 ( S i = − 3 / 2 ), there is another spin j , where j = i + 1 and S j = 1 / 2 ( S j = − 1 / 2 ), such that the absolute value of the magnetization per spin is one.