Presence or absence of order by disorder in a highly frustrated region of the spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices

Emergence of quantum spin frustration in spin-1/2 Ising-Heisenberg model on a decorated honeycomb lattice

We study the spin-1/2 Ising-XXZ model on a decorated honeycomb lattice composed of five spins per unit cell, one Ising spin, and four Heisenberg spins. This model involving the Heisenberg exchange interaction is one of the few models that can be exactly solvable through the generalized star-triangle transformation. The significance of this model is its close relationship to the fully decorated quantum Heisenberg honeycomb lattice since 4/5 of the particles are Heisenberg spins. We investigate the phase diagram at zero temperature and identify a relevant quantum spin frustrated phase resulting from the contribution of quantum Heisenberg exchange interaction. We obtain an exact residual entropy for the quantum spin frustrated phase, which coincides with the residual entropy of the antiferromagnetic spin-1/2 Ising model on a triangular lattice. We also thoroughly explore its thermodynamic properties, focusing mainly on the frustrated region such as entropy, specific heat, spontaneous magnetization, and critical temperature under several conditions.

Interaction-generated frustration in the ferromagnetic spin system on the kagome lattice: Exact analysis on the star kagomelike recursive lattice

Frustration effects caused by the presence of the six-site interaction in the ferromagnetic spin-1/2 Ising system on the kagome lattice are investigated in detail using the star kagomelike recursive lattice approximation. It is shown that although the model always exhibits the existence of only two standard phases (the ferromagnetic phase and the paramagnetic one) separated by the curve of the second-order phase transitions, depending on the value of the multisite interaction, the ferromagnetic phase splits into three different ground states in the zero-temperature limit with different magnetization and thermodynamic properties. The free energy of the model is derived, the residual entropies of all ground states are determined, and it is shown that the presence of the six-site multisite interaction leads to the formation of two highly macroscopically degenerated ground states in the studied ferromagnetic system, one of which is realized only for unique ratio of the six-site interaction to the ferromagnetic interaction. It is demonstrated that the existence of this highly macroscopically degenerated single-point-like ground state leads to appearance of the Schottky anomaly in the low-temperature behavior of the specific heat capacity in the vicinity of this ground state. It is also shown that the simultaneous presence of the frustration and of the second-order phase transitions in the studied model is responsible for the existence of even three local maxima in the temperature behavior of the specific heat capacity.

Ground state and thermodynamic properties of spin-1/2 isosceles Heisenberg triangles for V_{6}-like magnetic molecules

The spin-1/2 Hamiltonian for two coupled isosceles Heisenberg triangles, which is well suited for describing the V_{6}-type magnetic molecules, is studied by exact diagonalization. The quantum phase transition diagram, at zero temperature, is obtained as a function of the theoretical parameters. The zero temperature magnetization is also obtained as a function of the external magnetic field. The thermodynamic behavior of the magnetization, entropy, susceptibility, and specific heat, as a function of temperature, are also computed and the corresponding magnetocaloric effect analyzed for various values of the Hamiltonian parameters.

Nature of intermediate magnetization plateaus of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice resembling a triangulated kagome lattice

The spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice is exactly solved in a magnetic field within the framework of the generalized star-triangle transformation and the method of exact recursion relations. The generalized star-triangle transformation establishes an exact mapping correspondence with the effective spin-1/2 Ising model on a triangular Husimi lattice with a temperature-dependent field, pair and triplet interactions, which is subsequently rigorously treated by making use of exact recursion relations. The ground-state phase diagram of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice, which bears a close resemblance with a triangulated kagomé lattice, involves, in total, two classical and three quantum ground states manifested in respective low-temperature magnetization curves as intermediate plateaus at 1/9, 1/3, and 5/9 of the saturation magnetization. It is verified that the fractional magnetization plateaus of quantum nature have character of either dimerized or trimerized ground states. A low-temperature magnetization curve of the spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice resembling a triangulated kagome lattice may exhibit either no intermediate plateau, a single 1/3 plateau, a single 5/9 plateau, or a sequence of 1/9, 1/3, and 5/9 plateaus depending on a character and relative size of two considered coupling constants.

Frustration phenomenon in the spin-1/2 Ising-Heisenberg planar model of inter-connected trigonal bipyramid structures

Ground-state and finite-temperature properties of the exactly solvable mixed spin-1/2 Ising-Heisenberg planar model composed of identical trigonal bipyramids that are arranged into a regular archimedean lattice are examined with the aim to clarify the frustration phenomenon at zero and finite temperatures. It is shown that the ground-state spin frustration persists even far above the second-order phase transition. If the interaction ratio between the Heisenberg and Ising exchange interactions is close enough to the ground-state boundaries between the neighboring phases, a remarkable re-entrance of the (non-)frustrated spin arrangement of the Heisenberg spins can be observed around the critical temperature of the model. It is also evidenced that entropy and specific heat show pronounced temperature variations not only around the critical temperature, but also in low-temperature regime if values of the interaction parameters are taken from neighborhood of the ground-state phase transitions, where energies of the neighboring phases are very close.

Interchain interaction effect on the magnetic properties of azurite material

Considering the interchain exchange interaction through dimer and monomer in the azurite, a two-dimensional Ising-Heisenberg model with dimer and monomer interlacing arrangement is established, and the magnetic and thermodynamic properties are calculated by Monte Carlo method. In the ground state, as the magnetic field increases from zero, the system changes from quantum antiferromagnetic (QAF) state with monomer in antiferromagnetic state and dimer in spin singlet to the quantum ferrimagnetism (QFI) state with monomer in saturated state and dimer in spin singlet, and finally reaches the saturated spin state (SP). In the QFI state, system shows 1/3 magnetization plateau. Starting from the QAF phase closing to the boundary with QFI phase, the specific heat and magnetic susceptibility of the system with temperature show beaks in the low temperature region, corresponding phase change, and in the whole range of temperature they may present double peak structure. Starting from the two phases of QFI and SP near the boundary between them, the magnetic susceptibility and specific heat with temperature also show peak, and the corresponding phase transition temperature is symmetry with respect to the phase boundary. Comparing with the specific heat data in the experiment, we conjecture the strength of the interchain interaction of azurite material is about half of the dimer interaction.

Phase transitions of antiferromagnetic Ising spins on the zigzag surface of an asymmetrical Husimi lattice

An asymmetrical two-dimensional Ising model with a zigzag surface, created by diagonally cutting a regular square lattice, has been developed to investigate the thermodynamics and phase transitions on surface by the methodology of recursive lattice, which we have previously applied to study polymers near a surface. The model retains the advantages of simple formulation and exact calculation of the conventional Bethe-like lattices. An antiferromagnetic Ising model is solved on the surface of this lattice to evaluate thermal properties such as free energy, energy density and entropy, from which we have successfully identified a first-order order-disorder transition other than the spontaneous magnetization, and a secondary transition on the supercooled state indicated by the Kauzmann paradox.

Chaotic spin-spin entanglement on a recursive lattice

We propose an exactly solvable multisite interaction spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice for the rigorous studies of chaotic entanglement. By making use of the generalized star-triangle transformation, we map the initial model onto an effective Ising one on a Husimi lattice, which we solve then exactly by applying the recursive method. Expressing the entanglement of the Heisenberg spins, that we quantify by means of the concurrence, in terms of the magnetic quantities of the system, we demonstrate its bifurcation and chaotic behavior. Furthermore, we show that the underlying chaos may slightly enhance the amount of the entanglement and present on the phase diagram the transition lines from the uniform to periodic and from the periodic to chaotic regimes.