J. Roberto Viana

The quantum spin-1/2?J1?J2 antiferromagnet on a stacked square lattice: a study of effective-field theory in a finite cluster

The ground state phase diagram of the quantum spin-1/2 Heisenberg antiferromagnet in the presence of nearest-neighbor (J(1)) and next-nearest-neighbor (J(2)) interactions (J(1)-J(2) model) on a stacked square lattice, where we introduce an interlayer coupling through nearest-neighbor bonds of strength J(), is studied within the framework of the differential operator technique. The Hamiltonian is solved by effective-field theory in a cluster with N=4 spins (EFT-4). We obtain the sublattice magnetization m(A) for the ordered phases: antiferromagnetic (AF) and collinear (CAF-collinear antiferromagnetic). We propose a functional for the free energy Ψ(μ)(m(μ)) (μ=A, B) to obtain the phase diagram in the λ-α plane, where λ=J()/J(1) and α=J(2)/J(1). Depending on the values of λ and α, we found different ordered states (AF and CAF) and a disordered state (quantum paramagnetic (QP)). For an intermediate region α(1c)(λ) < α < α(2c)(λ) we observe a QP phase that disappears for λ below some critical value λ(1)≈0.67. For α < α(1c)(λ) and α > α(2c)(λ), and below λ(1), we have the AF and CAF semi-classically ordered states, respectively. At α=α(1c)(λ) a second-order transition between the AF and QP states occurs and at α=α(2c)(λ) a first-order transition between the AF and CAF phases takes place. The boundaries between these ordered phases merge at the critical end point CEP≡(λ(1), α(c)), where α(c)≈0.56. Above this CEP there is again a direct first-order transition between the AF and CAF phases, with a behavior described by the point α(c) independent of λ ≥ λ(1).

QUALITATIVE ASPECTS OF THE PHASE DIAGRAM OF J1 J2 MODEL ON THE CUBIC LATTICE

The qualitative aspects of the phase diagram of the Ising model on the cubic lattice, with ferromagnetic (F) nearest-neighbor interactions (J1) and antiferromagnetic (AF) next-nearest-neighbor couplings (J2) are analyzed in the plane temperature versus α, where α = J2/|J1| is the frustration parameter. We used the original Wang–Landau sampling (WLS) and the standard Metropolis algorithm to confront past results of this model obtained by the effective-field theory (EFT) for the cubic lattice. Our numerical results suggest that the predictions of the EFT are in general qualitatively correct, but the low-temperature re-entrant behavior, observed in the frontier separating the F and the collinear order, is an artifact of the EFT approach and should disappear when we consider Monte Carlo (MC) simulations of the model. In addition, our results indicate that the continuous phase transition between the F and the paramagnetic (P) phases, that occurs for 0.0 ≤α< 0.25, belongs to the universality class of the three-dimensional pure Ising Model.

The quantum spin-1/2 frustrated Heisenberg model on a stacked square lattice: a spin wave theory study

The ground state phase diagram and staggered magnetization of the quantum spin-1/2 Heisenberg models in the presence of nearest-neighbor (J1) and next-nearest-neighbor (J2) interactions (J1–J2 model) on a stacked square lattice, where we introduce an interlayer coupling through nearest-neighbor bonds of strength , are investigated by using linear spin wave theory. We analyze the order parameter mA for the ordered phases: antiferromagnetic (AF, J1 > 0), ferromagnetic (F, J1 0 (AF) that disappears for λ below some critical value . For α α2c(λ), and below λ1, we have the AF and CAF semi-classically ordered states, respectively. At α = α1c(λ) a second-order transition between the AF and QP states occurs and at α = α2c(λ) a first-order transition between the AF and CAF phases takes place. The boundaries between these ordered phases merge at the critical end point—, where αc = 1/2. Above this CEP there is again a direct first-order transition between the AF and CAF phases, with a behavior governed by the point αc independently of λ ≥ λ1. For J1 0 the QP intermediate region was not observed; only a small region of the disordered state (QP) was predicted in the two-dimensional limit (λ = 0).

A new effective correlation mean-field theory for the ferromagnetic spin-1 Blume–Capel model in a transverse crystal field

A new approximation technique is developed so as to study the quantum ferromagnetic spin-1 Blume–Capel model in the presence of a transverse crystal field in the square lattice. Our proposal consists of approaching the spin system by considering islands of finite clusters whose frontiers are surrounded by noninteracting spins that are treated by the effective-field theory. The resulting phase diagram is qualitatively correct, in contrast to most effective-field treatments, in which the first-order line exhibits spurious behavior by not being perpendicular to the anisotropy axis at low-temperatures. The effect of the transverse anisotropy is also verified by the presence of quantum phase transitions. The possibility of using larger sizes constitutes an advantage to other approaches where the implementation of larger sizes is computationally costly.

The magnetic susceptibility on the transverse antiferromagnetic Ising model: Analysis of the reentrant behavior

We study the three-dimensional antiferromagnetic Ising model in both uniform longitudinal (

First-order phase transition in the quantum spin glass at T=0

H

Three-dimensional Ising model with nearest- and next-nearest-neighbor interactions.

) and transverse (

Phase diagram of the Ising antiferromagnet with nearest-neighbor and next-nearest-neighbor interactions on a square lattice

\Omega

Anisotropy effects in frustrated Heisenberg antiferromagnets on a square lattice

) magnetic fields by using the effective-field theory with finite cluster

Study of the first-order transition in the spin-1 Blume–Capel model by using effective-field theory

N=1