We numerically investigate the non-equilibrium critical dynamics in three-dimensional anisotropic antiferromagnets in the presence of an external magnetic field. The phase diagram of this system exhibits two critical lines that meet at a bicritical point. The non-conserved components of the staggered magnetization order parameter couple dynamically to the conserved component of the magnetization density along the direction of the external field. Employing a hybrid computational algorithm that combines reversible spin precession with relaxational Monte Carlo updates, we study the aging scaling dynamics for the model C critical line, identifying the critical initial slip, autocorrelation, and aging exponents for both the order parameter and conserved field, thus also verifying the dynamic critical exponent. We further probe the model F critical line by investigating the system size dependence of the characteristic spin wave frequencies near criticality, and measure the dynamic critical exponents for the order parameter including its aging scaling at the bicritical point.
Classical anisotropic XY antiferromagnets in a field on square and simple cubic lattices are studied using mainly Monte Carlo simulations. While in two dimensions the ordered antiferromagnetic and spin--flop phases are observed to be separated by a narrow disordered phase, a line of direct transitions of first order between the two phases and a bicritical point are found in three dimensions. Results are compared to previous findings.
We present a method that optimizes the aspect ratio of a spatially anisotropic quantum lattice model during the quantum Monte Carlo simulation, and realizes the virtually isotropic lattice automatically. The anisotropy is removed by using the Robbins-Monro algorithm based on the correlation length in each direction. The method allows for comparing directly the value of critical amplitude among different anisotropic models, and identifying the universality more precisely. We apply our method to the staggered dimer antiferromagnetic Heisenberg model and demonstrate that the apparent non-universa…
We develop the field theory of antiferromagnets to layered structures on BCT crystal lattices with nearest-neibour and next-nearest-neighbour ferro- and/or antiferromagnetic interactions. For this aim the field theoretical counterpart of a lattice Heisenberg model is derived by standard theoretical methods: Hubbard-Stratonovich transformation and a generalized mean-field approach. We shown that the inter-layer interactions are a pure thermal fluctuation effect whereas the ground state is characterized by a perfect in-layer antiferromagnetic order and a lack of inter-layer coupling. This is a d…
The spin-1/2 anisotropic Heisenberg model with antiferromagnetic exchange interactions in the presence of a external magnetic field and a Dzyaloshinskii-Moriya interaction is studied by employing the usual mean-field approximation. The magnetic properties are obtained and it is shown that only second-order phase transitions take place for any values of the theoretical Hamiltonian parameters. Contrary to previous results from effective field theory, no anomalies have been observed at low temperatures. However, some re-entrancies still persist in some region of the phase diagram.
We study classical and quantum Heisenberg antiferromagnets with exchange anisotropy of XXZ-type and crystal field single-ion terms of quadratic and cubic form in a field. The magnets display a variety of phases, including the spin-flop (or, in the quantum case, spin-liquid) and biconical (corresponding, in the quantum lattice gas description, to supersolid) phases. Applying ground-state considerations, Monte Carlo and density matrix renormalization group methods, the impact of quantum effects and lattice dimension is analysed. Interesting critical and multicritical behaviour may occur at quant…
Global phase diagram and six-state clock universality behavior in the triangular antiferromagnetic Ising model with anisotropic next-nearest-neighbor coupling: Level-spectroscopy approach
The spectral properties of the spin-1/2 Heisenberg antiferromagnet on an anisotropic triangular lattice in a magnetic field are investigated using a weak-interchain-coupling approach combined with exact solutions of a chain. Dominant modes induced by interchain interactions in a magnetic field behave as quasiparticles which show distinctive features such as anomalous incommensurate ordering and high-energy modes. In terms of them, various unusual features observed in the anisotropic triangular antiferromagnet Cs_2CuCl_4 in a magnetic field are quantitatively explained in a unified manner.
In the paper the phase diagram of $J_1-J_2$ frustrated antiferromagnet with spin $S=1$ and single-ion anisotropy is studied on the planar quadratic lattice in the cluster approximation. The Bogolyubov inequality is adopted for the Gibbs energy calculation for the case of $2 \times 2$ and $4 \times 4$ clusters. On this basis, the ranges of existence of the anfiferromagnetic, superantiferromagnetic and paramagnetic phases are investigated for the antiferromagnetic nearest-neighbour ($J_1<0$) and next-nearest-neighbour ($J_2<0$) interactions. In particular, the occurrence of tricritical and tripl…
We study the correlation function of middle spins, i. e. of spins on intermediate sites between two adjacent parallel lattice axes, of the spatially anisotropic Ising antiferromagnet on the kagome lattice. It is given rigorously by a Toeplitz determinant. The large-distance behaviour of this correlation function is obtained by analytic methods. For shorter distances we evaluate the Toeplitz determinant numerically. The correlation function is found to vanish exactly on a line J_d(T) in the T-J (temperature vs. coupling constant) phase diagram. This disorder line divides the phase diagram into …
We use numerical transfer-matrix methods, together with finite-size scaling and conformal invariance concepts, to discuss critical properties of two-dimensional honeycomb-lattice Ising spin-1/2 magnets, with couplings which are antiferromagnetic along at least one lattice axis, in a uniform external field. We focus mainly on the shape of the phase diagram in field-temperature parameter space; in order to do so, both the order and universality class of the underlying phase transition are examined. Our results indicate that, in one particular case studied, the critical line has a horizontal sect…
We have studied the anisotropic three-dimensional nearest-neighbor Ising model with competitive interactions in an uniform longitudinal magnetic field $H$. The model consists of ferromagnetic interaction $J_{x}(J_{z})$ in the $x(z)$ direction and antiferromagnetic interaction $J_{y}$ in the $y$ direction. We have compared our calculations within a effective-field theory in clusters with four spins (EFT-4) in the simple cubic (sc) lattice with traditional Monte Carlo (MC) simulations. The phase diagrams in the $h-k_{B}T/J_{x}$ plane ($h=H/J_{x}$) were obtained for the particular case $λ_{1}=J_{…
Magnetic frustrations and dimensionality play an important role in determining the nature of the magnetic long-range order and how it melts at temperatures above the ordering transition $T_N$. In this work, we use large-scale Monte Carlo simulations to study these phenomena in a class of frustrated Ising spin models in two spatial dimensions. We find that the melting of the magnetic long-range order into an isotropic gas-like paramagnet proceeds via an intermediate stage where the classical spins remain anisotropically correlated. This correlated paramagnet exists in a temperature range $T_N <…
The phase diagram of the spin-1/2 Heisenberg antiferromagnet on an anisotropic triangular lattice of weakly coupled chains, a model relevant to Cs2CuCl4, is investigated using a renormalization group analysis, which includes marginal couplings important for connecting to numerical studies of this model. In particular, the relative stability of incommensurate spiral spin-density order and collinear antiferromagnetic order is studied. While incommensurate spiral order is found to exist over most of the phase diagram in the presence of a Dzyaloshinskii-Moriya (DM) interaction, at small interchain…
We study the S=1 Heisenberg antiferromagnet on a spatially anisotropic triangular lattice by the numerical diagonalization method. We examine the stability of the long-range order of a three-sublattice structure observed in the isotropic system between the isotropic case and the case of isolated one-dimensional chains. It is found that the long-range-ordered ground state with this structure exists in the range of 0.7 \simle J_2/J_1 \le 1, where J_1 is the interaction amplitude along the chains and J_2 is the amplitude of other interactions.
We introduce a minimal spin model for describing the magnetic properties of $\mathrm{CuCrO_2}$. Our Monte Carlo simulations of this model reveal a rich magnetic field induced phase diagram, which explains the measured field dependence of the electric polarization. The sequence of phase transitions between different mutiferroic states arises from a subtle interplay between spatial and spin anisotropy, magnetic frustration and thermal fluctuations. Our calculations are compared to new measurements up to 92 T.
It is known that there is no phase transition down to zero temperature in the antiferromagnetic Ising model on spatially anisotropic triangular lattices, in which the exchange coupling of one direction is stronger than those of other two directions. In the model, the low-temperature physics is governed by domain-wall excitations (defects) residing on bonds of the strong-coupling direction. In this letter, we show that an additional small attractive interaction between defects (a ferromagnetic next-nearest-neighbor interaction in the weak-coupling direction) leads to a Berezinskii-Kosterlitz-Th…
We consider analytically and numerically an anisotropic spin-$\frac{1}{2}$ delta-chain (sawtooth chain) with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interactions. For certain values of the interactions a lowest one-particle band becomes flat and there is a class of localized-magnon eigenstates which form a ground state with a macroscopic degeneracy. In this case the model depends on a single parameter which can be chosen as the anisotropy of the exchange interactions. When this parameter changes from zero to infinity the model interpolates between the one-dim…
Anisotropic antiferromagnets in an external magnetic field show a rich variety of different ground states meeting in transition lines and multicritical points. We study the dependence of the ground states of these systems in the three dimensional space on physical parameters as exchange, single ion and cubic anisotropy. One identifies four different ground states: the paramagnetic (PM), the antiferromagnetic (AF), the spin flop (SF) and the biconical (BC) ground state. In the case of absence of a cubic anisotropy the transition lines separating the different ground states can be calculated ana…
Spin liquids occuring in 2D frustrated spin systems were initially assumed to appear at strongest frustration, but evidence grows that they more likely intervene at transitions between two different types of order. To identify if this is more general, we here analyze a generalization of the spatially anisotropic triangular lattice (SATL) with antiferromagnetic Heisenberg interactions, the spatially \emph{completely} anisotropic triangular lattice (SCATL). Using Takahashi's modified spin-wave theory, complemented by exact diagonalizations, we find indications that indeed different kinds of orde…
Motivated by experiments on non-magnetic triangular-lattice Mott insulators, we study one candidate paramagnetic phase, the columnar dimer (or valence-bond) phase. We apply variants of the bond-operator theory to a dimerized and spatially anisotropic spin-1/2 Heisenberg model and determine its zero-temperature phase diagram and the spectrum of elementary triplet excitations (triplons). Depending on model parameters, we find that the minimum of the triplon energy is located at either a commensurate or an incommensurate wavevector. Condensation of triplons at this commensurate-incommensurate tra…
Magnetic phase diagram of a spatially anisotropic, frustrated spin-1/2 Heisenberg antiferromagnet on a stacked square lattice is investigated using second-order spin-wave expansion. The effects of interlayer coupling and the spatial anisotropy on the magnetic ordering of two ordered ground states are explicitly studied. It is shown that with increase in next nearest neighbor frustration the second-order corrections play a significant role in stabilizing the magnetization. We obtain two ordered magnetic phases (Neel and stripe) separated by a paramagnetic disordered phase. Within second-order s…
The effects of quantum fluctuations due to directional anisotropy and frustration between nearest neighbors and next-nearest neighbors of the quantum spin-1/2 Heisenberg antiferromagnet on a square lattice are investigated using spin-wave expansion. We have calculated the spin-wave energy dispersion in the entire Brillouin zone, renormalized spin-wave velocities, and the magnetization up to second order in 1/S expansion for the antiferromagnetic Neel and collinear antiferromagnetic stripe phases. It is shown that the second-order corrections become significant with increase in frustration. Wit…
