Critical behavior and spatial crossover in the frustrated antiferromagnetic Heisenberg model on a triangular lattice

The critical properties of the three-dimensional frustrated Heisenberg model on a layered triangular lattice with variable interplane exchange interaction have been investigated by the replica Monte Carlo method. All main magnetic and chiral critical exponents have been calculated. It is found that a decrease in the interlayer exchange leads to crossover from the three-to two-dimensional critical behavior.     

Topological defects and magnetization processes for the triangular lattice of ising particles with an antiferromagnetic interaction

For the frustrated triangular lattice of Ising magnetic moments with an antiferromagnetic interaction, which is in a state with two sublattices, a new type of topological defects with zero energy in the approximation of the interaction between only the nearest-neighbors has been found. These defects have a nonzero magnetic moment, and the magnetization in a low field occurs via the formation of a system of such defects. These properties are valid for a 2D superstructure in the form of a triangular lattice of single-domain magnetic particles with perpendicular anisotropy and dipole coupling.     

Topological defects and magnetization processes for the triangular lattice of ising particles with an antiferromagnetic interaction

JETP Letters - For the frustrated triangular lattice of Ising magnetic moments with an antiferromagnetic interaction, which is in a state with two sublattices, a new type of topological defects...     

Incommensurate-commensurate phase transitions in an anisotropic antiferromagnetic model on triangular lattice

An anisotropic antiferromagnetic model on a triangular lattice with competing interactions is investigated by the cluster transfer-matrix method. A phase diagram with ferrimagnetic, incommensurate, and disordered phases is found. Three order parameters are introduced. At commensurate-incommensurate and incommensurate-disorder phase transition lines two of them change in continuous and one in discontinuous way.     

Phase transitions in the antiferromagnetic ising model on a square lattice with next-nearest-neighbor interactions

The phase transitions in the two-dimensional Ising model on a square lattice are studied using a replica algorithm, the Monte Carlo method, and histogram analysis with allowance for the next-nearest-neighbor interactions in the range 0.1 ≤ r < 1.0. A phase diagram is constructed for the dependence of the critical temperature on the next-nearest-neighbor interaction. A second-order phase transition is detected in this range and the model under study.     

Phase transitions in the two-dimensional antiferromagnetic Potts model on a triangular lattice

Phase transitions and thermodynamic properties in the two-dimensional three-state antiferromagnetic Potts model on a triangular lattice are investigated using the Monte Carlo method and the histogram analysis of the data. It is shown that pronounced first-order phase transitions are observed in this model for systems with rather large linear dimensions (L > 120). No first-order PTs are observed for systems with L < 120.     

Critical phenomena for a triangular spin lattice I: Triplet interactions

Critical phenomena in an Ising-like spin system on a triangular lattice are studied by means of the renormalization theory. The critical indices of the critical point due to triplet interactions are determined approximately, in fair agreement with the exponents, known from the exact solution due to Baxter and Wu. The cross-over from triplet critical behavior to ferromagnetic (nearest neighbor) critical behavior is calculated.     

The density of states for an antiferromagnetic Ising model on a triangular lattice

The Wang-Landau algorithm is an efficient Monte Carlo approach to the density of states of a statistical mechanics system. The estimation of state density would allow the computation of thermodynamic properties of the system over the whole temperature range. We apply this sampling method to study the phase transitions in a triangular Ising model. The entropy of the lattice at zero temperature as well as other thermodynamic properties is computed. The calculated thermodynamic properties are explained in the context of the magnetic phase transition.      

Study of critical properties of the frustrated antiferromagnetic Heisenberg model on a triangular lattice

The replica Monte Carlo method has been applied to study critical properties of the three-dimensional frustrated antiferromagnetic Heisenberg model on a layered triangular lattice. Magnetic and chiral critical exponents for this model have been calculated within the finite-size scaling theory. The data for this model have been analyzed for the first time taking into account corrections to scaling. It has been shown that the critical behavior of the frustrated antiferromagnetic Heisenberg model on the triangular lattice differs from the critical behavior of the pure Heisenberg model and is independent of the type of interlayer exchange interaction.     

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.     

Octupolar order in the multiple spin exchange model on a triangular lattice

We show how a gapless spin liquid with hidden octupolar order arises in an applied magnetic field, in a model applicable to thin films of 3He with competing ferromagnetic and antiferromagnetic (cyclic) exchange interactions. Evidence is also presented for nematic--i.e., quadrupolar--correlations bordering on ferromagnetism in the absence of a magnetic field.     

Hubbard model on the triangular lattice: spiral order and spin liquid

We investigate the half-filled Hubbard model on an isotropic triangular lattice with the variational cluster approximation. By decreasing the on-site repulsion U (or equivalently increasing pressure) we go from a phase with long-range, three-sublattice, spiral magnetic order, to a nonmagnetic Mott insulating phase--a spin liquid--and then, for U less or similar to 6.7t, to a metallic phase. Clusters of sizes 3, 6, and 15 with open boundary conditions are used in these calculations, and an extrapolation to infinite size is argued to lead to a disordered phase at U = 8t, but to a spiral order at U greater or similar to 12.     

Magnon spin Nernst effect on the antiferromagnetic checkerboard lattice

In this paper we study topological effects in an anisotropic checkerboard antiferromagnetic lattice in the presence of the Dzyaloshinskii-Moriya interaction (DMI). The time reversal symmetry is broken by anisotropies in the Hamiltonian. However, in contrast to the honeycomb lattice, the DMI does not open a gap here. We calculate the energy spectrum of the magnons and the spin Nernst coefficient in the presence of a longitudinal temperature gradient.     

Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice

We show that the spin-liquid phase of the half-filled Hubbard model on the triangular lattice can be described by a pure spin model. This is based on a high-order strong coupling expansion (up to order 12) using perturbative continuous unitary transformations. The resulting spin model is consistent with a transition from three-sublattice long-range magnetic order to an insulating spin-liquid phase, and with a jump of the double occupancy at the transition. Exact diagonalizations of both models show that the effective spin model is quantitatively accurate well into the spin-liquid phase, and a comparison with the Gutzwiller projected Fermi sea suggests a gapless spectrum and a spinon Fermi surface.     

Monte Carlo simulations on magnetic behavior of a spin-chain system in triangular lattice doped with antiferromagnetic bonds

A three-dimensional Ising-like model doped with anti-ferromagnetic (AFM) bonds is proposed to investigate the magnetic properties of a doped triangular spin-chain system by using a Monte-Carlo simulation. The simulated results indicate that a steplike magnetization behavior is very sensitive to the concentration of AFM bonds. A low concentration of AFM bonds can suppress the stepwise behavior considerably, in accordance with doping experiments on Ca₃Co₂O₆. The analysis of spin snapshots demonstrates that the AFM bond doping not only breaks the ferromagnetic ordered linear spin chains along the hexagonal c-axis but also has a great influence upon the spin configuration in the ab-plane.      

Critical behavior of two-dimensional magnetic lattice gas model

Using Monte Carlo simulations and finite-size scaling, we investigate the critical behavior of two-dimensional magnetic lattice gas at densities ρ = 0.90, 0.95, 1.0. There is a ferromagnetic phase transition at each density. As expected, the critical temperature T _c depends on system density ρ. Unexpectedly, there is a density dependence of the critical exponent of correlation length ν. For densities ρ = 0.90,0.95,1.0, we obtain the inverse of critical exponent 1/ν = 0.835(5), 0.905(5), 1.00(1) respectively. It is found that the ratios of critical exponent β/ν and γ/ν of magnetization and susceptibility are independent of density.     

Phase transitions in a two-dimensional antiferromagnetic Potts model on a triangular lattice with next-nearest neighbor interactions

Phase transitions (PTs) and frustrations in two-dimensional structures described by a three-vertex antiferromagnetic Potts model on a triangular lattice are investigated by the Monte Carlo method with regard to nearest and next-nearest neighbors with interaction constants J₁ and J₂, respectively. PTs in these models are analyzed for the ratio r = J₂/J₁ of next-nearest to nearest exchange interaction constants in the interval |r| = 0–1.0. On the basis of the analysis of the low-temperature entropy, the density of states function of the system, and the fourth-order Binder cumulants, it is shown that a Potts model with interaction constants J₁ < 0 and J₂ < 0 exhibits a first-order PT in the range of 0 ? r < 0.2, whereas, in the interval 0.2 ? r ? 1.0, frustrations arise in the system. At the same time, for J₁ > 0 and J₂ < 0, frustrations arise in the range 0.5 < |r| < 1.0, while, in the interval 0 ? |r| ? 1/3, the model exhibits a second-order PT.     

Frustrated antiferromagnetic spin 1 Heisenberg model with single ion anisotropy on a simple cubic lattice

We study the effects of frustration between nearest, next-nearest neighbor and next-next-nearest neighbors (NNN) of the quantum S=1 anisotropic antiferromagnetic Heisenberg model on a simple cubic lattice with single ion anisotropy using the bond operator technique. We calculate the phase diagram at zero temperature and the gap as a function of temperature in the disordered paramagnetic phase.