Mean Field Renormalization Group Approach Research Articles

Site-diluted Blume–Capel model for the Fe–Al disordered alloys

The phase-diagram of a site-diluted spin-1 Blume–Capel model on a simple cubic lattice is studied by using the mean-field renormalization group approach in the pair approximation. The critical temperature has been obtained as function of the vacant sites concentration and the crystal-field. Considering exchange and superexchange interactions between Fe atoms we applied this model to the description of the thermodynamic properties of Fe–Al alloys. The experimental phase diagram has been adjusted with the theoretical parameters and compared with previous theoretical results.

Blume-Capel model for(Fe0.65Ni0.35)1−xMnxandFepAlqMnxalloys

A random-bond Blume-Capel model is proposed in order to study the ternary FeNiMn and FeAlMn alloys. The extended mean-field renormalization group approach and a variational procedure based on Bogoliubov inequality for the free energy are employed in the pair approximation. The phase diagrams are obtained for a symmetric distribution as well as for asymmetric distributions compatible to these alloys. The obtained phase diagram for the FeNiMn system is in a much better accord with the experimental data than the previous traditional mean-field renormalization group applied to the Ising model, mainly concerning the spin-glass and antiferromagnetic phases. Better results are also achieved for the order parameter of the FeAlMn alloys.

Two‐step mean‐field renormalization group results for the large square Ising clusters

AbstractA transfer matrix approach has been worked out to test the predictions of the improved three‐step mean‐field renormalization group approach to square Ising clusters with linear size up to L = 11. Performing the asymptotic analysis, the convergence of the finite‐size critical couplings and the critical exponents towards the exact values is shown.

Mean-field renormalization-group approach to the boson Hubbard model

We study the phase diagram of the boson Hubbard model at T=0 without disorder in a one-site and a two-site mean-field approximations. The two-site mean-field significantly improves the results compared to ordinary mean-field solutions and allows to use a simple scheme of mean-field renormalization group (MFRG). Some results obtained with MFRG are even better including the critical exponents for the density-driven transition between the Mott insulator and superfluid phases. However, when we evaluate critical exponents for transitions through the tip of the insulating lobes (special transitions without density change), we get similar exponents indicating that the MFRG apparently does not distinguish between both type of transitions and places them in the same universality class. The results for the first insulating lobe in d=1 and d=2 are in good agreement with a perturbative method and with the more reliable quantum Monte Carlo results. Our MFRG method provides analytical results for any lobe in any dimension and can be systematically improved if we consider larger clusters.

Phase diagram of the Kondo necklace: a mean-field renormalization group approach

In this paper we investigate the magnetic properties of heavy fermions in the antiferromagnetic and dense Kondo phases in the framework of the Kondo necklace model. We use a mean field renormalization group approach to obtain a temperature versus Kondo coupling $(T-J)$ phase diagram for this model in qualitative agreement with Doniach's diagram, proposed on physical grounds. We further analyze the magnetically disordered phase using a two-sites approach. We calculate the correlation functions and the magnetic susceptibility that allow to identify the crossover between the spin-liquid and the local moment regimes, which occurs at a {\em coherence} temperature.

Study of the crossover from 2 to 3 dimensions in the quantum spin- [formula omitted] anisotropic Heisenberg model

The phase diagram of the quantum spin- 1 2 anisotropic Heisenberg antiferromagnet is studied, within a mean-field renormalization-group approach in larger clusters. The model consists of an anisotropic cubic lattice, with in-plane J and inter-plane J′= λJ interactions. The dependence of the Néel temperature T N on the interlayer coupling λ and on the anisotropy parameter Δ ( Δ=0 and 1 correspond to the isotropic Heisenberg and Ising models, respectively) is obtained explicitly. We have shown that T N ( Δ, λ) is different from the Curie temperature T c ( Δ, λ), such that, at Δ c ( λ) [or λ c ( Δ)], T c = T N . The set of points Δ c ( λ) determine a characteristic frontier in the ( λ, Δ) plane, which separate three regimes. These are defined as: Curie, when T c > T N , Néel, when T c < T N , and mixed, where the two previous regimes coexist.

Critical behavior of heavy fermions within mean-field renormalization group approach

In order to study the critical behavior of heavy fermions near an antiferromagnetic quantum critical point, we apply the mean-field renormalization group to a simplified analog of the Kondo lattice, the Kondo necklace. We obtain the quantum critical point for different dimensions as well as the corresponding critical lines.

Reentrance in the phase diagram of the quantum spin 1/2 anisotropic Heisenberg antiferromagnet

The very recently improved treatment proposed by de Sousa and Plascak [Phys. Lett. A 237 (1997) 66], the mean field renormalization group (MFRG) approach used on the quantum spin 1/2 Heisenbeg antiferromagnet in two sublattices, is herein extended for larger clusters (two and four spins). The critical temperature for the ferromagnetic- T c(F) and antiferromagnetic- T N (AF) are obtained as a function of the anisotropy parameter ( Δ) on a square lattice. Within this approach, we find that T N is triple valued under certain condition of quantum competiting interaction ( Δ near of Δ c=0.18), suggesting the occurrence of reentrant behavior in the phase diagram. A preliminary analysis of finite size scaling in small cluster is presented, showing that the reentrance can be an effect of cluster finite size.

Phase diagram on the anisotropic quantum and classical Heisenberg models

The very recently improved treatment proposed by de Sousa and Plascak [Phys. Lett. A237 (1997) 66], the mean field renormalization group (MFRG) approach used on the quantum spin 1/2 Heisenberg antiferromagnet in two sublattices, is herein extended for larger clusters (two and four spins). The critical temperature for the ferromagnetic, T c(F) and antiferromagnetic, T N (AF) are obtained as a function of the interlayer parameter ( λ). Within this approach, we find that T N is double valued under certain condition of λ ( λ near of λ c=0.50), suggesting the occurrence of reentrant behavior in the phase diagram. We have also investigated the classical Heisenberg model and compared with results of Monte Carlo simulation. For the quantum Heisenberg model we compare with spin wave theory.

Crossover of the antiferromagnet Heisenberg to XY model

The criticality of the quantum anisotropic spin- 1 2 Heisenberg antiferromagnetic model is studied by the mean-field renormalization group (MFRG) approach. The critical temperature and the thermal exponent for the ferromagnetic (F) and antiferromagnetic (AF) cases are obtained as a function of the anisotropy parameter on a three-dimensional lattice. Particular attention is drawn to the difference between T c (F case) and T N (AF case). It is shown that in the quantum XY limit T c = T N , whereas T N > T c for the anisotropic Heisenberg model. We have also shown that the thermal critical exponent y t presents a small dependence on the type of interaction (F or AF) due to finite size effects.

The Random Mixed Spin-1/2 Heisenberg Ferromagnet

The mean field renormalization group approach has been used to investigate the random mixed spin-1/2 Heisenberg ferromagnet in the two and three-dimensions. The model can describe an isotropic Heisenberg material doped at random with Ising-like anisotropy impurity atoms. The critical surfaces are displayed graphically in the complete parameter space. The behaviours observed by incorporating the effect of randomness in the d =2 and d =3 systems are discussed.

Universality in the critical exponents δ and η

The critical exponents δ and η are obtained for the three-dimensional quantum spin- 1 2 anisotropic Heisenberg (QAH) model by the mean field renormalization group (MFRG) approach. The method is illustrated using its simplest approximation version in which clusters with N = 1,2,4 and 8 spins are used. The exponents δ and η are numerically estimated as a function of the anisotropy parameter Δ ( Δ = 0 and Δ = 1 correspond to the isotropic Heisenberg and Ising models, respectively) for all renormalization between clusters of sizes N ≥ 2. In all types of renormalizations the exponents analysed are independent of Δ. I also have studied the classical D-vector model by MFRG approach with clusters of sizes N′ = 1 and N = 2 spins. It was observed that δ and η do not depend on D and the numerical results are equivalent to the quantum case with the same clusters in MFRG approach. The results, qualitative and quantitative, of the present work are in excellent agreement with more accurate methods (Monte Carlo and series expansion).

Phase transition in the three-dimensional anisotropic Heisenberg antiferromagnetic model

The anisotropic Heisenberg model with spin- 1 2 and antiferromagnetic (AF) interaction is studied by the mean field renormalization group (MFRG) approach on a simple cubic lattice. This model in the ferromagnetic (F) limit was treated previously in the literature by Plascak [J. Phys. A 17 (1984) L597], but in this work we generalize the MFRG method for the model with AF interaction. The critical temperature and critical exponent are obtained as a function of the anisotropy parameter (Δ). The results obtained are compared with the critical behavior of the F model. We observe that T N is higher than T C, but the F and AF case present the same universality class.

Anisotropic triangular Ising model in the extended mean-field renormalization-group approach

Anisotropic triangular Ising model in the extended mean-field renormalization-group approach

The Application of Mean-Field Renormalization Group for A+B\rightarrow AB Reaction Model

We study A+B\rightarrow AB reaction model in one-dimension as an example of non-equilibrium systems by using mean-field renormalization group (MFRG) approach which relies on the comparison of different clusters of lattice sites. Time evolution of each state of clusters with different sizes, namely Master equations, are considered. For steady-state, phase transition and fixed points are investigated and compared with Monte Carlo simulation results.

Phase diagrams of the diluted and random-bond Ising model.

The quenched-bond disordered Ising model is studied by means of the mean-field renormalization-group approach. Besides dilution and ferromagnetic random bond, the probability distribution function also includes two extra competing random bonds which can be ferromagnetic or antiferromagnetic, depending on the sign of some competing parameters. The critical temperature against ferromagnetic bond concentration phase diagrams are analyzed for several values of the theoretical parameters.

Mean-field renormalization-group approaches to the surface on a semi-infinite Ising model with a random surface field.

Mean-field renormalization-group approaches to the surface on a semi-infinite Ising model with a random surface field.

Mean-field renormalization group for the boundary magnetization of strip clusters

We analyze in some detail a recently proposed transfer matrix mean field approximation which yields the exact critical point for several two dimensional nearest neighbor Ising models. For the square lattice model we show explicitly that this approximation yields not only the exact critical point, but also the exact boundary magnetization of a semi--infinite Ising model, independent of the size of the strips used. Then we develop a new mean field renormalization group strategy based on this approximation and make connections with finite size scaling. Applying our strategy to the quadratic Ising and three--state Potts models we obtain results for the critical exponents which are in excellent agreement with the exact ones. In this way we also clarify some advantages and limitations of the mean field renormalization group approach.

Charging effects and quantum crossover in granular superconductors.

The effects of the charging energy in the superconducting transition of granular materials or Josephson-junction arrays are investigated using a pseudo-spin-one model. Within a mean-field renormalization-group approach, we obtain the phase diagram as a function of temperature and charging energy. In contrast to earlier treatments, we find no sign of a reentrant transition in agreement with more recent studies. A crossover line is identified in the nonsuperconducting side of the phase diagram and along which we expect to observe anomalies in the transport and thermodynamic properties. We also study a charge ordering phase, which can appear for large nearest-neighbor Coulomb interaction, and show that it leads to first-order transitions at low temperatures. We argue that, in the presence of charge ordering, a nonmonotonic behavior with decreasing temperature is possible with a maximum in the resistance just before entering the superconducting phase.

The planar random anisotropy model: a mean-field renormalization group approach

We study the random anisotropy model, introduced to describe amorphous rare earth systems, using a mean-field renormalization group approach. For planar, classical spins, in three dimensions we find that the ferromagnetic phase is stable under a weak random anisotropy perturbation. We discuss the relevance of our results for transition metal-based amorphous ferromagnets with small concentrations of rare earth elements.