Antiferromagnetic XY Model Research Articles

The antiferromagnetic xy model on the triangular lattice: topological singularities

We study the discrete-to-continuum variational limit of the antiferromagnetic XY model on the two-dimensional triangular lattice in the vortex regime. Within this regime, the spin system cannot overcome the energetic barrier of chirality transitions, hence one of the two chirality phases is prevalent. We find the order parameter that describes the vortex structure of the spin field in the majority chirality phase and we compute explicitly the $\Gamma$-limit of the scaled energy, showing that it concentrates on finitely many vortex-like singularities of the spin field.

The antiferromagnetic XY model on the triangular lattice: chirality transitions at the surface scaling

We study the discrete-to-continuum variational limit of the antiferromagnetic XY model on the two-dimensional triangular lattice. The system is fully frustrated and displays two families of ground states distinguished by the chirality of the spin field. We compute the Gamma -limit of the energy in a regime which detects chirality transitions on one-dimensional interfaces between the two admissible chirality phases.

Random-bond disorder in two-dimensional noncollinear XY antiferromagnets: From quasi-long-range order to spin glass

We study effects of quenched bond disorder in frustrated easy-plane antiferromagnets in two space dimensions, using a combination of analytical and numerical techniques. We consider local-moment systems which display non-collinear long-range order at zero temperature, with the antiferromagnetic triangular-lattice XY model as a prime example. We show that (i) weak bond disorder transforms the clean ground state into a state with quasi-long-range order, and (ii) strong bond disorder results in a short-range-ordered glassy ground state. Using extensive Monte Carlo simulations, we also track the fate of the quasi-long-range-ordered phase at finite temperature and the associated Kosterlitz-Thouless-like transition. Making contact with previous studies of disordered XY models, we discuss similarities and differences concerning the interplay of disorder and frustration. Our results are also of relevance to non-collinear Heisenberg magnets in an external magnetic field.

Phase transitions in the frustrated antiferromagnetic XY model on the triangular lattice

Phase transitions and thermodynamics properties of the frustrated antiferromagnetic XY (FAXY) model have been investigated near the two transition temperatures. We found that the Kosterlitz-Thouless (KT) transition corresponding to the rotational U(1) symmetry breaking and the Ising-like (I) transition corresponding to the reflection Z2 symmetry breaking occur at two-separate transition temperatures, Tkt < TI. These temperatures lie close to each other, however in our results the separation is obvious. Our results show the order parameters as a function of temperature and we also estimate the critical exponents, β, α, γ, η and ν. The critical exponent ν indicates that the Ising-like transition is inconsistent with the Ising universality class.

Complexity of the XY antiferromagnet at fixed magnetization

We prove that approximating the ground energy of the antiferromagnetic XY model on a simple graph at fixed magnetization (given as part of the instance specification) is QMA-complete. To show this, we strengthen a previous result by establishing QMAcompleteness for approximating the ground energy of the Bose-Hubbard model on simple graphs. Using a connection between the XY and Bose-Hubbard models that we exploited in previous work, this establishes QMA-completeness of the XY model.

Phase transitions and order-by-quantum disorder for the antiferromagnetic XY model in the checkerboard lattice

In this work we have studied the phases of the XY antiferromagnetic model in the checkerboard lattice (the two-dimensional analog of the pyrochlore lattice). Using the traditional linear spin–wave approximation, we obtain a transition from an order to a disordered phase in some critical value rc=J′/J. The phase transition occurs due to quantum fluctuations. However, when we consider higher order perturbations the scenario is entirely different. We have applied the Self-Consistent Harmonic Approximation method and the results show that quantum perturbations induce long-range spin–spin correlations even above the critical point rc. This is a typical feature of order-by-quantum disorder when the system chooses one of the many classical ground states to occupy. We have also determined the thermal phase transitions similar to the Berezinskii–Kosterlitz–Thouless phase transition and the action of a single-ion anisotropy, responsible for a Quantum Phase Transition at zero temperature.

Chiral symmetry breaking in FAXY model with roughness exponent method

Chiral symmetry breaking in the frustrated antiferromagnetic XY (FAXY) model on a two-dimensional triangular lattice is investigated. The roughness exponent method is used instead of the standard Metropolis method. Spin configurations are mapped to adatoms on a solid-on-solid (SOS) growth model. Statistical properties of the grown film surface are analyzed. Results show that the chiral transition can be indicated by the sharp increase in the roughness of the film morphologies. The critical temperature at the transition can be identified either by the peak of the noise-reduced interface width (W∗) or the peak of the noise-reduced roughness exponent (α∗). The critical temperature and exponent (ν) obtained here are consistent with those obtained from conventional methods.

Behaviors of lattice distortions in the spin 1/2 antiferromagnetic XY model with quasiperiodic modulation

The behaviors of lattice distortions in the spin 1/2 antiferromagnetic XY model with Thue-Morse quasiperiodic modulation are investigated by the method of exact diagonalization. It is found that the lattice distortion at each site has the character intermediate between the periodic and random systems. For weaker or stronger quasiperiodic modulation, the lattice distortion may increase or decrease with strengthening of the modulation amplitude, respectively. The results also indicate that the energy gaps of ground states are strongly affected by the quasiperiodic modulation

TELESCOPIC LINKAGES AND A TOPOLOGICAL APPROACH TO PHASE TRANSITIONS

AbstractA topological approach to the theory of equilibrium phase transitions in statistical physics is based on the topological hypothesis, which claims that phase transitions are due to changes of the topology of suitable submanifolds in the configuration space. In this paper we examine in detail the antiferromagnetic mean-field XY model and study the topology of the subenergy manifolds. The latter can be interpreted mechanically as the configuration space of a linkage with one telescopic leg. We use methods of Morse theory to describe explicitly the Betti numbers of this configuration space. We apply these results to the antiferromagnetic mean-field XY model and compute the exponential growth rate of the total Betti number. Previous authors studied the Euler characteristic rather than the total Betti number. We show that in the presence of an external magnetic field the model undergoes a single ‘total Betti number phase transition’.

The ground state properties of the S = 1/2 antiferromagnetic XY model with quasiperiodic modulation

The low-energy properties of the S = 1/2 antiferromagnetic XY model with quasiperiodic modulation are investigated for the consideration of spin–phonon coupling. It is found that the lattice distortion at every site displays a self-similar character, which is induced by quasiperiodic modulation. As quasiperiodic modulation is strengthened, the average lattice distortion may decrease and increase for strong and weak enough spin–phonon coupling, respectively. Correspondingly, the scaling behavior of the energy gap in this system is also strongly dependent on the spin–phonon coupling.

Spin-dynamics simulations of the triangular antiferromagneticXYmodel

Using Monte Carlo and spin-dynamics methods, we have investigated the dynamic behavior of the classical, antiferromagnetic XY model on a triangular lattice with linear sizes $L&lt;~300.$ The temporal evolutions of spin configurations were obtained by solving numerically the coupled equations of motion for each spin using fourth-order Suzuki-Trotter decompositions of exponential operators. From space- and time-displaced spin-spin correlation functions and their space-time Fourier transforms we obtained the dynamic structure factor $S(\mathbf{q},w)$ for momentum $\mathbf{q}$ and frequency $\ensuremath{\omega}.$ Below ${T}_{\mathrm{KT}}$ (Kosterlitz-Thouless transition), both the in-plane ${(S}^{\mathrm{xx}})$ and out-of-plane ${(S}^{\mathrm{zz}})$ components of $S(\mathbf{q},\ensuremath{\omega})$ exhibit very strong and sharp spin-wave peaks. Well above ${T}_{\mathrm{KT}},$ ${S}^{\mathrm{xx}}$ and ${S}^{\mathrm{zz}}$ apparently display a central peak, and spin-wave signatures are still seen in ${S}^{\mathrm{zz}}.$ In addition, we also observed an almost dispersionless domain-wall peak at high $\ensuremath{\omega}$ below ${T}_{c}$ (Ising transition), where long-range order appears in the staggered chirality. Above ${T}_{c},$ the domain-wall peak disappears for all q. The line shape of these peaks is captured reasonably well by a Lorentzian form. Using a dynamic finite-size scaling theory, we determined the dynamic critical exponent $z=1.002(3).$ We found that our results demonstrate the consistency of the dynamic finite-size scaling theory for the characteristic frequency ${\ensuremath{\omega}}_{m}$ and the dynamic structure factor $S(\mathbf{q},\ensuremath{\omega})$ itself.

Phase transitions in the antiferromagneticXYmodel with akagomélattice

The ground state of the antiferromagnetic XY model with a kagome lattice is characterized by a well developed accidental degeneracy. As a consequence the phase transition in this system consists in unbinding of pairs of fractional vortices. Addition of the next-to-nearest neighbors (NNN) interaction leads to stabilization of the long-range order in chirality (staggered chirality). We show that the phase transition, related with destruction of this long-range order, can happen as a separate phase transition below the temperature of the fractional vortex pairs unbinding only if the NNN coupling is extremely weak, and find how the temperature of this transition depends on coupling constants. We also demonstarte that the antiferromagnetic ordering of chiralities and, accordingly, the presence of the second phase transition are induced by the free energy of spin wave fluctuations even in absence of the NNN coupling.

Violation of ensemble equivalence in the antiferromagnetic mean-field XY model

It is well known that long-range interactions pose serious problems for the formulation of statistical mechanics. We show in this paper that ensemble equivalence is violated in a simple mean-field model of N fully coupled classical rotators with repulsive interaction (antiferromagnetic XY model). While in the canonical ensemble the rotators are randomly dispersed over all angles, in the microcanonical ensemble a bi-cluster of rotators separated by angle $\pi$, forms in the low energy limit. We attribute this behavior to the extreme degeneracy of the ground state: only one harmonic mode is present, together with N-1 zero modes. We obtain empirically an analytical formula for the probability density function for the angle made by the rotator, which compares extremely well with numerical data and should become exact in the zero energy limit. At low energy, in the presence of the bi-cluster, an extensive amount of energy is located in the single harmonic mode, with the result that the energy temperature relation is modified. Although still linear, $T = \alpha U$, it has the slope $\alpha \approx 1.3$, instead of the canonical value $\alpha =2$.

Skyrmion lattice melting in the quantum Hall system

The melting and magnetic disordering of the skyrmion lattice in the quantum Hall system at filling factor $\nu\approx 1$ are studied. A Berezinskii-Kosterlitz-Thouless renormalization group theory is employed to describe the coupled magnetic and translational degrees of freedom. The non-trivial magnetic properties of the skyrmion system stem from the in-plane components of the non-collinear magnetization in the vicinity of skyrmions, which are described by an antiferromagnetic XY model. In a Coulomb gas formulation the `particles' are the topological defects of the XY model (vortices) and of the lattice (dislocations and disclinations). The latter frustrate the antiferromagnetic order and acquire fractional vorticity in order to minimize their energy. We find a number of melting/disordering scenarios for various lattice types. While these results do not depend on a particular model, we also consider a simple classical model for the skyrmion system. It results in a rich T=0 phase diagram. We propose that the triangular and square skyrmion lattices are generically separated by a centered rectangular phase in the quantum Hall system.

Phase diagrams of the S= quantum antiferromagnetic XY model on the triangular lattice in magnetic fields

We study the S=1/2 quantum antiferromagnetic XY model on finite triangular lattices with N sites in both longitudinal and transverse magnetic fields. We calculate physical quantities in the ground state using a diagonalization for spins $N \leq 27$, and those at finite temperatures using a quantum transfer Monte Carlo method for $N \leq 24$. In the longitudinal magnetic field, the long-range chiral order parameter seems to have a finite, nonzero value at low temperatures suggesting the occurrence of a classical umbrella-type phase. In the transverse magnetic field, the 1/3-plateau of the magnetization curve appears even at low temperatures, in contrast with the classical model. The magnetic field dependences of the order parameters suggest that the chiral-ordered, the ferrimagnetic, and the spin flop phases appear successively as the magnetic field is increased. The transition temperatures are estimated from the peak position of the specific heat, and the phase diagrams are predicted in both longitudinal and transverse magnetic fields.

Anisotropic antiferromagnetic XY-model of classical Heisenberg spins on a triangular lattice

Abstract We obtain a phase diagram of an anisotropic antiferromagnetic XY-model of classical Heisenberg spins on a triangular lattice by calculating the average values of x-component and y-component of spins, the chirality, angles between averaged spins on sublattices and the specific heat by means of Monte Carlo simulations. It turns out that the system has two phase transition temperatures: one for the Kosterlitz-Thouless-type phase transition and the other for the Ising-type phase transition. These two phase transition temperatures are merged into one in the isotropic XY-model. We find that the chirality is a good order parameter at low temperatures even in the system with anisotropic interaction. For the system with isotropic interaction, the 120 degree structure persists as far as the chirality is non-zero.

Classical antiferromagnetic XY model with competing interaction

The mean-field analysis of the antiferromagnetic XY model on a square lattice under magnetic field is carried out. First and second nearest spin interactions are considered. The role played by competing and noncompeting interactions in the critical behavior of the system are studied. The phenomenon of a continuous degeneracy breaking effect due to temperature excitations and dilution is examined and discussed.

The dynamical mechanism of (111) surface reconstruction: frustration and vortex structures

In terms of the antiferromagnetic XY-model on a triangular lattice in two dimensions, the mechanisms of (111) surface reconstructions of homopolar semiconductors are reconsidered. The validity of the proposed model is examined by comparing it with several experimental results, with which satisfactory agreement is obtained. In particular, the present model leads to the stability of the 5*5 and the 7*7 structures as well as a high probability of the nucleation of the N*N dimer adatom stacking-fault reconstruction from an upper step edge.

Vortex dynamics in the classical two-dimensional antiferromagnetic XY model

We investigate the dynamics of the two-dimensional antiferromagnetic Heisenberg model with easy-plane exchange symmetry by explicitly calculating the dynamic correlation functions S αα( q , w), α = x, y, z. In addition to the spin waves we find also topological excitations, namely vortices which cause a Kosterlitz-Thouless phase transition at T KT. Our main interest is focused on the free vortices just above T KT where we developed a phenomenology based on a dilute gas of noninteracting vortices. With this ansatz we find central peaks in S αα( q , w) which are at different positions in q-space depending on whether the static vortex structure or the deviations from it due to a finite velocity dominates the correlations. We compare these results with a combined Monte Carlo Molecular Dynamics simulation on a 100 × 100 square lattice. We find a good agreement between our theory and the simulations and we obtain from this comparison explicit values for the vortex correlation length and the vortex average velocity.

Low Temperature Properties of One-Dimensional ClassicalXYModel with Frustration

An antiferromagnetic classical XY model with the nearest-neighbor interaction 2 J and the next-nearest-neighbor interaction δ J on a one-dimensional lattice is investigated in the low temperature limit. We obtain the asymptotic behaviors at long distances, of the two-spin correlation function for δ>1/2 and of the chirality-chirality correlation function for δ=1. The behavior of the latter correlation function is shown to be similar to the one of the two-spin correlation function for the Ising model with the nearest-neighbor interaction J /2 on a one-dimensional lattice.