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 properties of a frustrated Heisenberg model on a stacked triangular lattice with allowance for second-nearest neighbor interaction

The critical properties of the three-dimensional antiferromagnetic Heisenberg model are investigated using the Monte Carlo method with allowance for second-nearest neighbor interaction. Pseudo-universal critical behavior of this model is observed for small lattices. A complete set of the main static magnetic and chiral indices is calculated with the use of finite-dimensional scaling theory.     

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.     

Phase transitions and critical properties of the frustrated Heisenberg model on a layer triangular lattice with next-to-nearest-neighbor interactions

The critical behavior of the three-dimensional antiferromagnetic Heisenberg model with nearest-neighbor (J) and next-to-nearest-neighbor (J ₁) interactions is studied by the replica Monte Carlo method. The first-order phase transition and pseudouniversal critical behavior of this model are established for a small lattice in the interval R = |J ₁/J| = 0?C0.115. A complete set of the main static magnetic and chiral critical indices is calculated in this interval using the finite-dimensional scaling theory.     

Investigation of the critical properties of the frustrated Heisenberg model on a triangular lattice by the Monte Carlo method

The critical properties of the 3D frustrated antiferromagnetic Heisenberg model on a triangular lattice have been investigated by the replica Monte Carlo method. All main magnetic and chiral critical indices were calculated using the finite-size scaling theory. It is found that the class of universality of the critical behavior of the model studied depends on the type of interplane exchange interaction.     

Monte Carlo investigation of phase transitions in the frustrated Heisenberg model on a triangular lattice

The critical properties and phase transitions of the three-dimensional frustrated antiferromagnetic Heisenberg model on a triangular lattice have been investigated using the Monte Carlo method with a replica algorithm. The critical temperature has been determined and the character of the phase transitions has been analyzed using the method of fourth-order Binder cumulants. A second-order phase transition has been found in the three-dimensional frustrated Heisenberg model on a triangular lattice. The static magnetic and chiral critical exponents of the heat capacity α, the susceptibility γ and γ _k , the magnetization β and β _k , the correlation length ν and ν _k , as well as the Fisher exponents η and η _k , have been calculated in terms of the finite-size scaling theory. It has been demonstrated that the three-dimensional frustrated antiferromagnetic Heisenberg model on a triangular lattice forms a new universality class of the critical behavior.     

Computer simulation of the frustrated antiferromagnetic Heisenberg model on a layered triangle lattice

Critical properties of the 3D frustrated Heisenberg model on a triangle latticeare investigated using a replica Monte-Carlo method that considers the interaction between next nearest neighbors. Static magnetic and chiral critical indices for heat capacity α, susceptibility γ, γ _k , magnetization β, β _k , and correlation radius ν are calculated using the theory of finite-size scaling.     

The frustrated Heisenberg antiferromagnet on the honeycomb lattice: J1-J2 model

We study the ground-state phase diagram of the frustrated spin-[Formula: see text] antiferromagnet with J(2) = xJ(1) > 0 (J(1) > 0) on the honeycomb lattice, using the coupled-cluster method. We present results for the ground-state energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. We find a paramagnetic PVBC phase for x(c(1)) < x < x(c(2)), where x(c(1)) ≈ 0.207 ± 0.003 and x(c(2)) ≈ 0.385 ± 0.010. The transition at x(c(1)) to the Néel phase seems to be a continuous deconfined transition (although we cannot exclude a very narrow intermediate phase in the range 0.21 ? x ? 0.24), while that at x(c(2)) is of first-order type to another quasiclassical antiferromagnetic phase that occurs in the classical version of the model only at the isolated and highly degenerate critical point [Formula: see text]. The spiral phases that are present classically for all values x > 1/6 are absent for all x ? 1.     

A frustrated heisenberg antiferromagnet on a triangular lattice with next-nearest neighbor interactions

Using the Monte Carlo method, we study the critical properties of the three-dimensional frustrated Heisenberg model on a triangular lattice with allowance for next-nearest neighbor interactions. Using the theory of finite-size scaling, we calculate the static magnetic and chiral critical exponents of heat capacity α, susceptibility γ, γ _k , magnetization β, β _k , and correlation length ν.     

Quadrupolar phases of the s=1 bilinear-biquadratic Heisenberg model on the triangular lattice

Using mean-field theory, exact diagonalizations, and SU(3) flavor theory, we have precisely mapped out the phase diagram of the S = 1 bilinear-biquadratic Heisenberg model on the triangular lattice in a magnetic field, with emphasis on the quadrupolar phases and their excitations. In particular, we show that ferroquadrupolar order can coexist with short-range helical magnetic order, and that the antiferroquadrupolar phase is characterized by a remarkable 2/3 magnetization plateau, in which one site per triangle retains quadrupolar order while the other two are polarized along the field. Implications for actual S=1 magnets are discussed.     

Phase transitions in the antiferromagnetic Heisenberg model on a layered triangular lattice with the next-nearest neighbor interactions

Phase transitions in the three-dimensional antiferromagnetic Heisenberg model on a layered triangular lattice with the next-nearest neighbor interactions have been studied by the histogram Monte Carlo method. Phase transitions in this model have been studied in the range of the next-nearest neighbor interactions from 0.0 to 1.0. The first-order phase transition has been revealed in the considered interval in the studied model.     

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.