A.S.T. Pires

The phase diagram and critical properties of the two-dimensional anisotropic XY model

In this paper we present a study of the phase diagram and critical properties of the square-lattice quantum XY model, with a single-ion anisotropy and spin S = 1, as a function of the anisotropy parameter D. For D less than a critical value DC, which is the critical point for a quantum phase transition at T = 0, the model presents a Berezinskii–Kosterlitz–Thouless (BKT) transition. This region is adequately described by the self-consistent harmonic approximation. We show that, if we want to use a Schwinger boson theory in this region, we should include fluctuations around the mean-field approximation (which leads to a gauge field) to describe correctly the BKT transition. However both methods are inadequate to describe the large-D phase, and we show that this phase can be studied using the bond operator formalism which gives the correct behaviour for the correlation length as a function of the temperature in the critical point and above. Our results agree with scaling arguments.

Low-temperature spin transport in a S = 1 one-dimensional antiferromagnet

We study spin transport in the insulating antiferromagnet with S = 1 in one dimension. The spin conductivity is calculated, at zero temperature, using a modified spin wave theory and the Kubo formalism, within the ladder approximation. Two-magnon processes provide the dominant contribution to the spin conductivity. At finite temperature, free magnons are activated, and turn the system into a perfect spin conductor, i.e., the spin conductivity has a Drude form with infinite scattering time.

Phase diagrams of a two-dimensional Heisenberg antiferromagnet with single-ion anisotropy

Abstract A two-dimensional Heisenberg antiferromagnet with a single-ion anisotropy is studied in the presence of a uniform magnetic field along the easy axis. The concept of effective field-dependent anisotropy is applied to the theoretical description of the phase diagrams. We perform calculations using the self-consistent harmonic approximation to treat the XY phase and the Green function technique for the Ising phase. Monte Carlo simulations on L × L square lattices, with L =8,16,32 and 64, and with periodic boundary conditions were performed for the classical model. In order to test the validity of the effective anisotropy concept we compare our theoretical calculation with simulation data. We also calculate theoretically the phase diagram of the compound Rb 2 MnF 4 , a quasi-two-dimensional spin 5/2 antiferromagnet, finding good agreement with experimental data. Our estimates for the transition temperature of the compounds K 2 MnF 4 and Mn(HCOO) 2 ·2H 2 O, in zero magnetic field, are also in agreement with the experimental values.

A quantum self-consistent harmonic approximation

A self-consistent harmonic approximation is used to treat the low temperature limit of the one and two-dimensional, large S, easy plane magnets.

Low-temperature thermodynamic study of the diluted planar rotator model using a self-consistent harmonic approximation

Abstract The self-consistent harmonic approximation is used to study a dilute planar rotator model in two dimensions. The Kosterlitz–Thouless transition temperature is obtained as a function of p , where p is the concentration of links. The phase transition in the system is deduced from a deviation of the power law describing the decay of the phase correlation function and from a jump in the helicity modulus. Better results are obtained when vortex corrections are included.

Dynamics of the one-dimensional quantum antiferromagnet with Dzyaloshinski–Moriya interactions

Abstract The in-plane dynamical correlation function for the quantum one-dimensional antiferromagnet with a Dzyaloshinski–Moriya antisymmetric exchange term is calculated asymptotically exactly at low temperatures using a projection operator technique proposed by G. Reiter. The static correlation functions needed for the dynamics are evaluated using the harmonic approximation. Apart from a broadening of the spin-wave peak, the two-magnon processes give rise to additional resonances in the spectrum when the anisotropy parameter associated to the Dzyaloshinski–Moriya exchange is greater than the exchange constant.

Phase transitions in the two-dimensional Anisotropic Biquadratic Heisenberg Model

Abstract In this paper we study the influence of the single-ion anisotropy in the two-dimensional biquadratic Heisenberg model (ABHM) on the square lattice at zero and finite low temperatures. It is common to represent the bilinear and biquadratic terms by J 1 = J cos θ and J 2 = J sin θ , respectively, and the many phases present in the model as a function of θ are well documented. However we have adopted a constant value for the bilinear constant ( J 1 = 1 ) and small values of the biquadratic term ( | J 2 | J 1 ). Specially, we have analyzed the quantum phase transition due to the single-ion anisotropic constant D . For values below a critical anisotropic constant D c the energy spectrum is gapless and at low finite temperatures the order parameter correlation has an algebraic decay (quasi-long-range order). Moreover, in D D c phase there is a transition temperature where the quasi-long-range order (algebraic decay) is lost and the decay becomes exponential, similar to the Berezinski–Kosterlitz–Thouless (BKT) transition. For D > D c , the excited states are gapped and there is no spin long-range order (LRO) even at zero temperature. Using Schwinger bosonic representation and Self-Consistent Harmonic Approximation (SCHA), we have studied the quantum and thermal phase transitions as a function of the bilinear and biquadratic constants.

Spin dynamics in the two-dimensional spin-1/2 Heisenberg antiferromagnet

We present low-temperature dynamic properties of the quantum twodimensional antiferromagnetic Heisenberg model with spin S = 1/2. The calculation of the dynamic correlation function is performed by combining a projection operator formalism and the modified spin-wave theory (MSW), which gives a gap in the dispersion relation for finite temperatures. The so calculated dynamic correlation function shows a double peak structure. We also obtain the spin-wave damping and compare our results to some experimental data and theoretical results obtained by other authors using different approaches.

Planar vortex in two-dimensional XY ferromagnets with a nonmagnetic impurity potential

Using a model of nonmagnetic impurity potential, we have examined the behavior of planar vortex solutions in the classical two-dimensional XY ferromagnets in the presence of a spin vacancy localized out of the vortex core. Our results show that a spinless atom impurity gives rise to an effective potential that repels the vortex structure.

Dynamical correlation from topological solitons in two-dimensional anisotropic models

The structure and dynamics of soliton configurations are considered for a two-dimensional classical Heisenberg model in the XY-and Ising-like models. Using a phenomenology based on a dilute gas of mobile solitons we obtain a central peak (ω=0) for dynamical correlation functions.