Thermodynamical properties of the mixed spin Blume–Capel model with four-spin interactions

Exact phase diagram for the mixed spin-1/2 and spin-S Ising models on the square lattice

“…It has been obtained for arbitrary spins S (S>1/2) in the presence of a quadratic single-ion term acting upon S-spins. We showed that, in both cases (S integer and half-odd-integer), the current system exhibits only second order transition without tricritical behavior as suggested previously by approximated methods EFT [20] and FCA [21,22]. On the other hand, our exact results confirm those obtained using Monte Carlo simulations [16][17][18] and renormalization group method [19] did for S=1.…”

“…These results are depicted in figure 7. However, effective field theory (EFT) [20] and finite cluster approximation (FCA) [21,22] give wrong results for a coordination number greater than 3, since they predict the existence of a tricritical behavior. These wrong results arise from the decoupling approximations used for treating correlations between spins in those theories.…”

Dynamic phase diagrams of a ferrimagnetic mixed spin (1/2, 1) Ising system within the path probability method

“…The equilibrium properties of the mixed spin-(1/2, 1) Ising and its exact solution on different lattices have been studied in detail (see Refs. [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and references therein). It should be pointed out that the exact solution of mixed spin (1/2, 1) Ising model is studied in detail on a honeycomb and diced lattices [25][26][27].…”