Multicritical behavior of the antiferromagnetic spin-3/2 Blume-Capel model: Finite-size-scaling and Monte Carlo studies

Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of thes=3/2Ising model from renormalization-group theory

“…A single first-order boundary forms between the F 3 and F 1 ordered phases, disconnected from the second-order boundary to the D 3 and D 1 disordered phases. This phase diagram, for d = 3 from renormalizationgroup theory, agrees with the phase diagram previously found for d = 2 by finite-size scaling and Monte Carlo [10,11].…”

A study of the bilayer Bethe lattice for spin- Ising model

“…A few years later, the spin- 3 2 Hamiltonian with the uniaxial and biaxial anisotropy, anisotropic exchange and magnetic field was studied in the molecular field approximation [3] and then its quadrupole line and the double critical point is discussed by the use of the same approximation method [4]. Later, the study of spin- 3 2 models has been extended to many physical systems and for many physical reasons, that is spin- 3 2 Blume-Capel (BC) model on the honeycomb and square lattices within the statistical accuracy of the Bethe-Peierls approximation (or the correlated effective field treatment) [5] and only on the honeycomb lattice within the framework of an effective field theory based on the use of a probability distribution [6] was studied in detail, the model on the simple cubic lattice was also investigated by the two-spin cluster approximation in the cluster expansion method [7], the BC model was studied on the cubic, triangular, square and Kagome´lattices with arbitrary spin S, namely S ¼ 1; 3 2 and 2 using a two-spin cluster field theory [8], its phase diagrams for the spin- 3 2 BC model in two-dimension was explored by the conventional finite-size-scaling, conformal invariance, and Monte-Carlo (MC) simulations [9], the multicritical behavior of the antiferromagnetic BC model on a square lattice and in two dimensions were studied by using the MFA [10] and the transfer-matrix finite-sizescaling calculations and MC simulations [11], respectively, the quantum phase transition in spin- 3 2 was studied by using the vertex state models [12], the most general spin- 3 2 Ising model was investigated for the square lattice in the subspace of the four-dimensional space spanned by the coupling constants J, K, L and M and it is shown that this model is reducible to an eight-vertex model on a surface in the parameter space spanned by the coupling constants [13], the MC simulations and a density matrix [14] and a corner transfer renormalization group method [15] was also applied to a similar Hamiltonian of [13] and with the bilinear interaction and a random magnetic field on the honeycomb lattice was studied within the framework of the effective-field approximation based on the exact spin-identities and differential operator technique [16]. In addition to these, it is also shown that the spin- 3 2 Ising model is equivalent to the Ashkin-Teller...…”

Magnetic properties of the bond and crystal field dilution spin-3/2 Blume–Capel model in an external magnetic field

“…A variety of methods has been used to study the spin-3/2 BCM, i.e. mean field approximation [12], transfer matrix technique [13], finite-size scaling [14,15], Monte Carlo simulations [12,15], effective field theory [16,17], cluster variation method [18], thermodynamically self-consistent theory [19], the heating and cooling algorithms [2], exact recursion method [20,21] and so on.…”