The magnetic properties and phase diagrams of the mixed spin-1 and spin-1/2 Ising model on a checkerboard square structure have been studied using the Monte Carlo simulations based on the Metropolis update protocol. The system consists of four quartets of alternative spin configuration. The effect of the exchange interactions J and crystal field D on the magnetic properties, critical and compensation temperatures, susceptibility, and specific heat of the system have been investigated. The phase diagrams, T-J and T-D, for different values of the exchange interactions and crystal field have been examined. We found that the compensation temperature starts to evolve for J1 < 0.6 of the spin-1 assembly and for J2 > 1.6 for spin-1/2. On the other hand, the effect of ferrimagnetic coupling does not show any threshold value; in this case, the compensation temperature is constant. Regarding the crystal field strength, the threshold value of D > -0.8 has been observed. We obtain the N-, Q- and P-type compensation behaviors in the system. We have observed that the phase diagrams exhibit only a second-order phase transition to a paramagnetic phase; hence, the system does not show the tricritical point. The magnetic hysteresis cycles of the mixed spin-1 and spin-1/2 on a checkerboard square structure for different values of the exchange interactions, temperatures, and crystal fields have been found. Finally, the system exhibits the superparamagnetism behavior for a fixed value of the temperature and crystal field.
In the many fields in which the Ising model is applied nowadays, the spin variables are often assumed to be of spin-class $\{-1,1\}$ or $\{0,1\}$, even though for any mix of binary real valued spin-classes a proper Ising model distribution exists. Here we show that in their basis all these spin-classes are the same, as a simple expressions exist that allow us to transform the variables from one particular mix of spin-classes to any other combination, without changing the probabilities for the system states as a whole.
Phase transitions of the mixed spin-1/2 and spin-S Ising model on a three-dimensional decorated lattice with a layered structure
在一个精确映射到简单自旋1/2伊辛模型的框架下，研究了具有层状磁结构的三维缀饰晶格上自旋1/2和自旋S（S >= 1/2）混合伊辛模型的相变.对于混合自旋的分层伊辛模型，这种映射对应产生了合理的结果，或者通过采用正交晶格上自旋为1/2的伊辛模型的简化解[Z. D. Zhang，Philos.Mag.87（2007）5309-5419]或通过对四重晶格上的相应自旋1/2伊辛模型进行广泛的蒙特卡罗模拟。结果表明，临界行为显着依赖于轴向零场分裂参数，层间和层内相互作用的相对强度。引人注目的自发秩序捕获的“准1D”自旋系统中发现的相互作用参数的限制区域中，零场分裂参数的力量，所有整数值的装饰自旋对他们的“非磁性”的自旋状态。
Weak universality, bicritical points and reentrant transitions in the critical behaviour of a mixed spin-1/2 and spin-3/2 Ising model on the union jack (centered square) lattice
For the generalized Ising models with all possible interactions within a face of the square lattice the formulas for finding partition function and free energy per lattice site in the thermodynamic limit were derived on a certain, in the general case, 8-dimensional subset of exact disordered solutions of 10-dimensional set of the Hamiltonian's parameters. When a part of parameters are set to zero, as a consequence, the disorder solutions were got for the models with nearest, next-nearest-neighbor and the interaction of four spins in an external field and without an external field, triangular a…
The antiferromagnetic quantum Ising chain has a quantum critical point which belongs to the universality class of the transverse Ising model (TIM). When a longitudinal field ($h$) is switched on, the phase transition is preserved, which turns to first-order for $h/Γ\to \infty$, $Γ$ being the strength of the transverse field. Here we will re-examine the critical properties along the phase transition line. During a quantum block renormalization group calculation, the TIM fixed point for $h/Γ>0$ is found to be unstable. Using DMRG techniques, we calculated the entanglement entropy and the spin-sp…
Weak universal critical behaviour of the mixed spin-(1/2, S) Ising model on the union jack (centered square) lattice: integer versus half-odd-integer spin-S case
The mixed spin-(1/2, 3/2) Ising model on a decorated square lattice, which takes into account lattice vibrations of the spin-3/2 decorating magnetic ions at a quantum-mechanical level under the assumption of a perfect lattice rigidity of the spin-1/2 nodal magnetic ions, is examined via an exact mapping correspondence with the effective spin-1/2 Ising model on a square lattice. Although the considered magnetic structure is in principle unfrustrated due to bipartite nature of a decorated square lattice, the model under investigation may display anomalous spin frustration driven by a magnetoelas…
We used mean-field theory based on the Bogoliubov inequality for the Gibbs free energy to examine the magnetic properties of a mixed spin-5/2 and spin-7/2 Blume-Capel ferrimagnetic system. The thermal behaviours of the system magnetization are classified according to the extended Néel nomenclature. The system exhibits compensation phenomena where a complete cancellation of sublattice magnetizations is observed below the critical temperature. Temperature-dependent phase diagrams are constructed for the case of unequal sublattice crystal field interactions. Under appropriate conditions, our calc…
In this work, we have performed Monte Carlo simulations to study phase transitions in a mixed spin-1 and spin-3/2 Ising ferrimagnetic system on the square and cubic lattices and with two different single-ion anisotropies. This lattice is divided in two interpenetrating sublattices with spins $S^A = 1$ (states $\pm1$ and 0) on the sublattice $A$ and $S^B = 3/2$ (states $\pm 3/2$, $\pm 1/2$) on the sublattice $B$. We have used single-ion anisotropies $D_{A}$ and $D_{B}$ acting on the sites of the sublattice $A$ and $B$, receptively. We have determined the phase diagrams of the model in the tempe…
Exact solution of the mixed-spin Ising model on a decorated square lattice with two different kinds of decorating spins on horizontal and vertical bonds
With conformal-invariance methods, Burkhardt, Guim, and Xue studied the critical Ising model, defined on the upper half plane $y>0$ with different boundary conditions $a$ and $b$ on the negative and positive $x$ axes. For $ab=-+$ and $f+$, they determined the one and two-point averages of the spin $σ$ and energy $ε$. Here $+$, $-$, and $f$ stand for spin-up, spin-down, and free-spin boundaries, respectively. The case $+-+-+\dots$, where the boundary conditions switch between $+$ and $-$ at arbitrary points, $ζ_1$, $ζ_2$, $\dots$ on the $x$ axis was also analyzed. In this paper the alternating …
