Exact coexistence surfaces containing double critical points for a three-component solution on the Bethe,honeycomb, and square lattices

A model is considered in which the bonds of a lattice are covered by rodlike molecules. Neighboring molecular ends interact with orientation-dependent interactions. The model exhibits closed -loop phase diagrams and double critical points. Exact coexistence surfaces are calculated for the model on the Bethe, honeycomb, and square lattices. The nature of the doubling of the critical exponent near a double critical point is calculated. The behavior of the critical line in the neighborhood of a double critical point is calculated exactly.     

Monte Carlo study of the antiferromagnetical Ising model on a centred honeycomb lattice

We use the Monte Carlo method to study an antiferromagnetical Ising spin system on a centred honeycomb lattice, which is composed of two kinds of 1/2 spin particles A and B. There exist two different bond energies J_A-A and J_A-B in this lattice. Our study is focused on how the ratio of J_A-B to J_A-A influences the critical behaviour of this system by analysing the physical quantities, such as the energy, the order parameter, the specific heat, susceptibility, {etc} each as a function of temperature for a given ratio of J_A-B to J_A-A. Using these results together with the finite-size scaling method, we obtain a phase diagram for the ratio J_A-B / J_A-A. This work is helpful for studying the phase transition problem of crystals composed of compounds.     

Construction of phase diagrams for nanoscaled Ising thin films on the honeycomb lattice using cellular automata simulation approach

The phase diagrams of the three-layer Ising model on the honeycomb lattice with a diluted surface have been constructed using the probabilistic cellular automata based on Glauber algorithm. The effects of the exchange interactions on the phase diagrams have been investigated. A general mathematical expression for the critical temperature is obtained in terms of relative coupling r = J₁/J and Δ_s = (J_s/J) ? 1, where J and J_s represent the nearest neighbor coupling within inner- and surface-layers, respectively, and each magnetic site in the surface-layer is coupled with the nearest neighbor site in the inner-layer via the exchange coupling J₁. In the case of antiferromagnetic coupling between surface-layer and inner-layer, system reveals many interesting phenomena, such as the possibility of existence of compensation line before the critical temperature.     

Blume-Emery-Griffiths model on the honeycomb lattice

Exact results are obtained for a spin-1 system on the honeycomb lattice with the Blume-Emery-Griffiths Hamiltonian –/kT =J _i,j S _i S _j +Ki,jS _i ² _j ² – _i S _i ² +HS _i subject to the constraintK=–ln coshJ. ForJ>0, the system behaves like a spin-1/2 Ising ferromagnet with the free energy analytic everywhere except at the first-order phase boundaryH=0, tanhJ<(2+e )/ . Derivatives of the free energy across this boundary are discontinuous and we obtain the exact expression for the spontaneous magnetization. ForJ<0, the system can be transcribed into an antiferromagnetic spin-1/2 Ising model in a real magnetic field, and from this equivalence portions of the exact phase boundary are determined.     

Reentrant phase transitions and multicompensation points in the mixed-spin Ising ferrimagnet on a decorated Bethe lattice

A mixed-spin Ising model on a decorated Bethe lattice is rigorously solved by combining the decoration–iteration transformation with the method of exact recursion relations. Exact results for critical lines, compensation temperatures, total and sublattice magnetizations are obtained from a precise mapping relationship with the corresponding spin-1/2 Ising model on a simple (undecorated) Bethe lattice. The effect of next-nearest-neighbour interaction and single-ion anisotropy on magnetic properties of the ferrimagnetic model is investigated in particular. It is shown that the total magnetization may exhibit multicompensation phenomenon and the critical temperature vs. the single-ion anisotropy dependence basically changes with the coordination number of the underlying Bethe lattice. The possibility of observing reentrant phase transitions is related to a high enough coordination number of the underlying Bethe lattice.     

Effect of Bond-Diluted on Spin-3/2 Transverse Ising Model with Crystal Field

The magnetic properties of the bond-diluted spin-3/2 transverse Ising model with the presence of a crystalfield on the honeycomb lattice are studied within the framework of the effective field theory with correlations. Theinteractions Jij are assumed to be independent random variables with distribution P(Jij) ＝ pδ(Jij - J) + (1 - P)δ(Jij).     

The anti-ferromagnetic Ising model on the simplest pure Husimi lattice: An exact solution

The anti-ferromagnetic spin-1/2 Ising model on the pure Husimi lattice with three sites in the elementary polygon (p=3$p=3$) and the coordination number z=4$z=4$ is investigated. It represents the simplest approximation of the anti-ferromagnetic Ising model on the two-dimensional kagome lattice which takes into account effects of frustration. The exact analytical solution of the model is found and discussed. It is proven that the model does not exhibit the first order as well as the second order phase transitions. A detailed analysis of the magnetization properties is performed and the existence of the magnetization plateaus for low temperatures is shown. All possible ground states of the model are found and discussed.     

Effect of Bond-Diluted on Spin-3/2 Transverse Ising Model with Crystal Field

The magnetic properties of the bond-diluted spin-3/2 transverse Ising model with the presence of a crystal field on the honeycomb lattice are studied within the framework of the effective field theory with correlations. The interactions J_ij are assumed to be independent random variables with distribution P(J_ij)=pδ(J_ij-J)+(1-p)δ(J_ij).     

Light-induced unconventional Landau levels of ultracold fermions in a trilayer honeycomb lattice

The spectrum of cold fermionic atoms is studied in a trilayer honeycomb optical lattice subjected to a perpendicular effective magnetic field,which is created with optical means. In the low energy approximation,the spectrum shows unconventional Landau levels,which are proportional to the 3/2 power of integer numbers. The zoro modes exist and the quasiparticles are chiral. It is also proposed to identify the unconventional Landau levels via probing the dynamic structure factor of the system with Bragg spectr...     

Transport properties in the photonic super‐honeycomb lattice — a hybrid fermionic and bosonic system

We report on the transport properties of the super‐honeycomb lattice, the band structure of which possesses a flat band and Dirac cones, according to the tight‐binding approximation. The super‐honeycomb model combines the honeycomb lattice and the Lieb lattice and displays the properties of both. It also represents a hybrid fermionic and bosonic system, which is rarely seen in nature. By choosing the phases of input beams properly, the flat‐band mode of the super‐honeycomb lattice will be excited and the input beams will exhibit strong localization during propagation. On the other hand, if the modes of Dirac cones of the super‐honeycomb lattice are excited, one will observe conical diffraction. Furthermore, if the input beam is properly chosen to excite a sublattice of the super‐honeycomb lattice and the modes of Dirac cones with different pseudospins, e.g., by the three‐beam interference pattern, the pseudospin‐mediated vortices will be observed.

     

Magnetic phase structure on the Penrose lattice

The Ising model on a two-dimensional Penrose tiling is studied by means of the Migdal-Kadanoff scheme. This approximate renormalization method closely follows the inflation rules of the tiling, which are easily described in terms of Robinson triangles, and lead to the consideration of four types of nearest neighbor couplings. The ferromagnetic phase transition is similar to the usual one encountered on periodic lattices. When the couplings have both signs, the presence of frustration without randomness yields a fairly intricate phase diagram, essentially made up of two regions with a very complicated border. Region I consists of quasiferromagnetic models, which exhibit long-range order below some finite critical temperature. The models of region II are paramagnetic at nonzero (low) temperature, but may become ordered (reen-trant phases) in a higher temperature range.     

Exact thermodynamic behavior of a generalized spin-isospin ising system on the Bethe lattice

We study a generalized Ising system consisting of a Bethe lattice on every site of which two spin-1/2 and two isospin-1/2 (or atomic species A) states can be realized, the spin-species interacting with appropriate nearest neighbor couplings. The system is equivalent to that of four states per site and we obtain its exact thermodynamic behavior. The case of a fixed concentration of species is the annealed or liquid magnetic binary alloy. The temperature dependence of the short-range-order (SRO) parameter of such systems is obtained as an application of the theory and discussed in connection with relevant material from the literature. When fixing both the concentration and the nearest neighbor spatial correlation of the species, we obtain Eggarter's formulas for the frozen-in species problem, which therefore are only approximately valid even on the Bethe lattice.     

Critical behaviour of the ferromagnetic Ising model on a triangular lattice

We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined by generating accurate data for lattices with L= 8, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spin algorithm we employ has the advantages of both a Metropolis algorithm and a single-update method. Our study indicates that the transition is continuous at T_c= 3.6403({2}). A convincing finite-size scaling analysis of the model yields υ=0.9995(21), β / υ = 0.12400({17}), γ / υ = 1.75223(22), γ '/υ=1.7555(22), α/υ= 0.00077(420) (scaling) and α / υ = 0.0010(42) (hyperscaling). The present scheme yields more accurate estimates for all the critical exponents than the Monte Carlo method, and our estimates are shown to be in excellent agreement with their predicted values.     

Thermodynamics of a model wih interacting annealed bond impurities on the Bethe lattice

A magnetic model is considered consisting of annealed, mutually repelling ferromagnetic bond impurities in an antiferromagnetic host lattice. Using recurrence relation techniques, the grand-canonical version of this model is solved on the three-coordinated Bethe lattice. A generic phase diagram is obtained containing, apart from the usual ferro- and antiferromagnetic regimes, two distinct incommensurate phases as well as a period-four modulated phase. Evidence is obtained that in one of the two incommensurate phases impurity pairing occurs.     

The Ising model on the layered J1-J2 square lattice

We investigate the phase transitions in the Ising model on a layered square lattice with first-($J_1$) and second-($J_2$) neighbor intralayer interactions and interlayer couplings (J). The thermodynamics of the system is evaluated within a cluster mean-field approximation, which allows us to identify the nature of the thermally driven phase transitions hosted by the model. As a result, we find that interlayer couplings reduce the region of first-order phase transitions between paramagnetic and superantiferromagnetic states. We also find that the interlayer couplings reduce the frustration effects by reducing the entropy content of the low-temperature phases. Our results suggest that tricriticality is present in the special case $J=J_1$, which is in qualitative agreement with recent Monte Carlo simulations for the model.     

Exact equilibrium shapes of Ising crystals on triangular/honeycomb lattices

The anisotropic surface tension for an Ising system below the critical point on a triangular or a honeycomb lattice can be computed through duality. Using the Wulff construction, the equilibrium shape of a crystal (droplet of one phase inside a sea of the other) is found. An exact and simple equation for this shape is derived.     

Mixed spin-1 and spin-3/2 Ising system with two alternative layers of a honeycomb lattice within the effective-field theory

An effective-field theory with correlations is developed for a mixed spin-1 and spin-3/2 Ising system with two alternative layers of a honeycomb lattice. Spin-1 atoms and spin-3/2 atoms are distributed in alternative layers of a honeycomb lattice. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the interaction between the vertically aligned spins and adjacent spins are coupled either ferromagnetically or antiferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the temperature dependence of the total magnetization to find the compensation points and to determine the type of compensation behavior. We present the phase diagrams in different planes for h=0, and the phase diagrams contain the paramagnetic, nonmagnetic and ferrimagnetic phases. The system also presents a tricritical behavior besides multicritical point (A), isolated critical point (C) and double critical end point (B) depending on the interaction parameters.     

Spin-1/2 Ising model on a AFM/FM two-layer Bethe lattice in a staggered magnetic field

A bilayer spin-1/2 Ising model consisting of two superposed Bethe lattices with antiferromagnetic/ferromagnetic interactions is studied by the use of exact recursion relations in a pairwise approach in the presence of an external staggered magnetic field. Besides the ground state phase diagrams calculated in different possible planes of the model parameters space, the thermal variations of the order-parameters and the free energy are investigated to obtain the temperature-dependent phase diagrams of the model for different values of the coordination numbers q. Our calculations reveal that depending on the strength of the model parameters, the model exhibits a variety of interesting phase transitions and therefore phase diagrams.     

First order phase transitions in the antiferromagnetic Ising model on a pure Husimi lattice

The antiferromagnetic spin-1/2 Ising model on the pure Husimi lattice with three sites in the elementary polygon (p=3$p=3$) and the coordination number z=6$z=6$ is investigated which represents the simplest approximation of the antiferromagnetic Ising model on the regular triangular lattice which takes into account effects of geometric frustration. The region of parameters is found in which two physical phases coexist. In addition, the existence of the first order phase transitions between these two coexisting phases is demonstrated and investigated in detail. A detailed analysis of the magnetization properties of the model is performed and the existence of the magnetization plateaus for low temperatures is shown. All possible ground states of the model are found and discussed.