Journal of Statistical Mechanics Theory and Experiment
Single-ion anisotropy as the source of anomalies in thermodynamic properties of magnetic spin-1/2 − 1 mixed systems on square and simple cubic lattices
Abstract The influence of the single-ion anisotropy on the thermodynamic properties of ferromagnetic as well as ferrimagnetic spin-1/2 − 1 mixed systems on the square and simple cubic lattice is investigated in the framework of the exactly solvable Ising-like models on the corresponding recursive lattices. The exact solutions of the models are present in the form of the explicit expressions for the free energy per site as the functions of the coordinates of the fixed points of the corresponding systems of recursion relations. The phase diagrams of the models are determined and the existence of compensation temperatures in the ferrimagnetic cases are discussed. The equations that drive the positions of the critical points are derived. The existence of the tricritical behavior in the three-dimensional system on the simple cubic lattice and its nonexistence in the case of the two-dimensional system on the square lattice is demonstrated. It is shown that the presence of the single-ion anisotropy can naturally lead to the emergence of the thermodynamic anomalies typical for frustrated magnetic systems even in unfrustrated ferromagnetic systems on studied bipartite lattices. First of all, the studied models exhibit the formation of strict residual-entropy hierarchies between the neighboring ground states of the system of three different ground states. It is also shown that due to this behavior of the entropy the specific heat capacity of the models exhibit anomalous (Schottky) behavior at low temperatures in the vicinity of the values of the anisotropy parameter, for which highly macroscopically degenerated single-point-like ground states are formed.
Abstract The influence of the single-ion anisotropy on the thermodynamic properties of ferromagnetic as well as ferrimagnetic spin-1/2 − 1 mixed systems on the square and simple cubic lattice is investigated in the framework of the exactly solvable Ising-like models on the corresponding recursive lattices. The exact solutions of the models are present in the form of the explicit expressions for the free energy per site as the functions of the coordinates of the fixed points of the corresponding systems of recursion relations. The phase diagrams of the models are determined and the existence of compensation temperatures in the ferrimagnetic cases are discussed. The equations that drive the positions of the critical points are derived. The existence of the tricritical behavior in the three-dimensional system on the simple cubic lattice and its nonexistence in the case of the two-dimensional system on the square lattice is demonstrated. It is shown that the presence of the single-ion anisotropy can naturally lead to the emergence of the thermodynamic anomalies typical for frustrated magnetic systems even in unfrustrated ferromagnetic systems on studied bipartite lattices. First of all, the studied models exhibit the formation of strict residual-entropy hierarchies between the neighboring ground states of the system of three different ground states. It is also shown that due to this behavior of the entropy the specific heat capacity of the models exhibit anomalous (Schottky) behavior at low temperatures in the vicinity of the values of the anisotropy parameter, for which highly macroscopically degenerated single-point-like ground states are formed.
The mixed-spin-(1∕2,SB,SC) Ising model on a decorated square lattice with two different kinds of decorating spins SB and SC $({S}_{\mathrm{B}}\ensuremath{\ne}{S}_{\mathrm{C}})$ placed on its horizontal and vertical bonds, respectively, is exactly solved by establishing a precise mapping relationship with the corresponding spin-1∕2 Ising model on an anisotropic square (rectangular) lattice. The effect of uniaxial single-ion anisotropy acting on both types of decorating spins SB and SC is examined, in particular. If decorating spins SB and SC are integer and half-odd-integer, respectively, or if the reverse is the case, the model under investigation displays a very peculiar critical behavior that had bearing on the spontaneously ordered ``quasi-one-dimensional'' spin system, which appears as a result of the single-ion anisotropy strengthening. We have found convincing evidence that this remarkable spontaneous ordering virtually arises even though all integer-valued decorating spins tend toward their ``nonmagnetic'' spin state S=0 and the system becomes disordered only upon further increase of the single-ion anisotropy. The single-ion anisotropy parameter is also at an origin of various temperature dependences of the total magnetization when imposing the pure ferrimagnetic or the mixed ferro-ferrimagnetic character of the spin arrangement.
Within the framework of an effective field approximation, the effects of single-ion anisotropy and different trimodal transverse fields of two sublattices on the critical properties of the mixed spin-1/2 and spin-1 Ising system are investigated on the simple cubic lattice. A smaller single-ion anisotropy can magnify magnetic ordering phases and a larger one can depress magnetic ordering phase for T -Ω 1/2 space at low temperatures, while a smaller single-ion anisotropy can hardly change the value of critical transverse field for T -Ω 1 space. On the other hand, influences of two different trimodal transverse fields concentrations on tricritical points and magnetic ordering phases take on some interesting results in T - D space. The main reason comes from the common action of single-ion anisotropy, different transverse fields and two trimodal distributions.
The effect of uniaxial single-ion anisotropy on magnetic and critical properties of the mixed spin-1/2 and spin-S (S > 1/2) Ising model on a three-coordinated Bethe lattice is rigorously examined with the help of star-triangle transformation and exact recursion relations.In particular, our attention is focused on the ferrimagnetic version of the model, which exhibits diverse temperature dependences of the total and both sublattice magnetizations.It is shown that the critical behavior of the mixed-spin Ising model on the Bethe lattice basically depends on whether the quantum spin number S is integer or half-odd-integer.
Recently, it has been rigorously verified that several one-dimensional (1D) spin models may exhibit a peculiar pseudo-transition accompanied with anomalous response of thermodynamic quantities in a close vicinity of pseudo-critical temperature. In the present work we will introduce and exactly solve a mixed spin-(1/2,1) Ising-Heisenberg double-tetrahedral chain in an external magnetic field as another particular example of 1D lattice-statistical model with short-range interactions that displays a pseudo-transition of this type. The investigated model exhibits at zero temperature three ferrimagnetic phases, three frustrated phases, and one saturated paramagnetic phase. The ground-state phase diagram involves five unusual interfaces (phase boundaries), at which the residual entropy per site equals to a larger entropy of one of two coexisting phases. Four such interfaces are between a non-degenerate ferrimagnetic phase and a macroscopically degenerate frustrated phase, while one interface is between two non-degenerate ferrimagnetic phases. Though thermal excitations typically destroy all fingerprints of zero-temperature phase transitions of 1D lattice-statistical models with short-range forces, the mixed spin-(1/2,1) Ising-Heisenberg double-tetrahedral chain is quite robust with respect to thermal excitations and it displays peculiar pseudo-transitions close to all five aforementioned interfaces.
Purpose The authors investigate the magnetic properties of a mixed spin-3/2 and spin-2 Blume-Capel model on square and cubic lattices with two different single-ion anisotropies. Design/methodology/approach To study the critical behavior of a mixed spin-3/2 and spin-2 system, the authors have used a real space renormalization group approximation and specifically the Migdal-Kadanoff technique. The authors give the phase diagrams for two different cases: (1) on the (Δ/|J|, 1/|J|) plane with ΔA = ΔB = Δ, and (2) on the (ΔA/|J|, 1/|J|) and (ΔB/|J|, 1/|J|) planes for selected values of ΔB/|J| and ΔA/|J|, respectively. Findings The phase diagrams obtained show that the system exhibits both second- and first-order phase transitions as well as tricritical points for some values of the anisotropies. Moreover, using the variation of the free energy and its derivative at low temperatures, the authors have seen the appearance of first-order transitions at very low temperatures. Originality/value Few investigations of mixed spin-3/2 and spin-2 systems with crystal field have been realized. For this reason, the authors use the renormalization group approach to complete the work done on these systems. In absence of an exact solution, this contributes to the synthesis of the approximation results on mixed spins models.
An exactly solvable variant of a mixed spin-(1/2,1) Ising-Heisenberg diamond chain is considered. Vertical spin-1 dimers are taken as quantum ones with Heisenberg bilinear and biquadratic interactions and with single-ion anisotropy, while all interactions between spin-1 and spin-1/2 residing on the intermediate sites are taken in the Ising form. The detailed analysis of the T=0 ground-state phase diagram is presented. The phase diagrams have been shown to be rather rich, demonstrating a large variety of ground states: a saturated one, three ferrimagnetic ones with magnetization equal to 3/5, and another four ferrimagnetic ground states with magnetization equal to 1/5. There are also two frustrated macroscopically degenerated ground states that could exist at zero magnetic filed. Solving the model exactly within a classical transfer-matrix formalism we obtain exact expressions for all thermodynamic functions of the system. The thermodynamic properties of the model have been described exactly by exact calculation of the partition function within the direct classical transfer-matrix formalism.