Mean Field Renormalization Group Method Research Articles

Diluted and random-bond Ising model and the Mean-field renormalization group (MFRG) method for the interpretation of the magnetic phase diagram of the FexMn0.6−xAl0.4 alloy series

Diluted and random-bond Ising model and the Mean-field renormalization group (MFRG) method for the interpretation of the magnetic phase diagram of the FexMn0.6−xAl0.4 alloy series

Characterization of magnetic phases in the Fe xMn 0.65−xAl 0.35 disordered alloys

Melted alloys of the Fe x Mn 0.65− x Al 0.35 disordered system, 0.25⩽ x⩽0.65, were experimentally studied by Mössbauer spectrometry, vibrating sample magnetometry and AC magnetic susceptibility. All the alloys exhibit the BCC structure with a nearly constant lattice parameter (2.92 Å). Mössbauer studies at room temperature (RT) show that in the 0.25 ⩽ x⩽0.45 range the alloys are paramagnetic (P) while in the 0.50⩽ x⩽0.65 range, they are ferromagnetic. At 77 K, Mössbauer studies show that the alloy with x = 0.25 presents weak magnetic character that is consistent with an antiferromagnetic (AF) behavior due to the high Mn content, while those with 0.30⩽ x⩽0.40 are paramagnetic, and those in the 0.45⩽ x⩽0.65 range are ferromagnetic (F) with a mean field increasing with the Fe content. Hysteresis cycles at RT prove the paramagnetic character of the alloys between x = 0.25 and 0.40 and the ferromagnetic character for x ⩾ 0.45 . Complementary measurements using AC magnetic susceptibility permit a magnetic phase diagram to be proposed, with the P phase for high temperature and all the compositions, the AF phase for low Fe content and at low temperature, the F phase for high Fe content above RT and the spin glass phase for all the compositions and at temperatures lower than 46 K. In addition, the mean field renormalization group (MFRG) method, applied to a random competitive and site dilute Ising model with nearest-neighbor, gives rise to magnetic phase diagram, which fairly agrees with previous experimental one.

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.

Site-diluted quantum Heisenberg spin model applied to the magnetic properties of Fe–Al disordered alloys

In this work we present a theoretical study of the magnetic behavior of disordered Fe–Al alloys on the basis of a simple-diluted quantum Heisenberg spin model with the assumption that the exchange interaction J depends on the Al concentration q. We calculated the critical temperature and exponents through the mean field renormalization group method. An acceptable fit to the experimental phase diagram for Al concentration in the range 0.30⩽q⩽0.45 is obtained.

Multicritical Points from Mean Field Renormalization Group

The mean field renormalization group method is extended to study tri-critical phenomena. By taking into account the third-order terms in the expansion of the magnetizations of the different clusters with respect to the symmetry breaking fields, together with the scaling assumption of the magnetization at a first-order fixed point, one additional equation is obtained which locates, in an unique manner, the tricritical point. This approach is applied in the study of the classical spin-σ Blume–Capel model and the quantum spin-1/2 anisotropic Heisenberg model in the presence of a transverse field as well as with Dzyaloshinsky–Moriya interactions.

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.

Study of the mean field renormalization group method with the Tsallis statistics

The phase transition of the Ising model in d-dimensional lattice is reanalyzed by using the mean field renormalization group method within the Tsallis generalization of the Boltzmann-Gibbs statistics (BGS). The critical temperature ( T c) is obtained explicitly for a general dimension d and a factor q present in the generalized statistics for clusters of one ( N′ = 1) and two ( N = 2) spind. In the q → 1 limit, the present work reduces to the results of Indekeu et al. (J. Phys. A 15 (1982) L291) with the usual BGS. For a linear chain ( d = 1), the system presents a phase transition for q ≠ 1. When we have q⪢1, T c( d, q) is proportional to the factor q, in accordance with the result of mean field approximation.

Mean-field renormalization group for the q-state clock spin-glass model

The mean-field renormalization group is used to study the phase diagrams of a d-dimensional q-state clock spin-glass model. We found, for q = 3 clock, the transition from paramagnet to spin glass is an isotropic spin-glass phase, but for q = 4 clock, the transition from paramagnet to spin glass is an anisotropic spin-glass phase. However, for q ⩾ 5 clock, the result of anisotropic spin-glass phase depends on the temperature and the distribution of random coupling. While the coordinate number approaches infinity, the critical temperature evaluated by the mean-field renormalization group method is equal to that by the replica method.

Numerical Calculations for the Surface on a Semi-Infinite Ising Model with a Random Surface Field11The project supported by National Natural Science Foundation of China and the Chinese Academy of Sciences through Grant LWTZ-1298

We study the critical behavior of the surface on a semi-infinite simple cubic lattice Ising model with a bimodal random surface field by large cell mean-field renormalization group method and Monte Carlo simulations. Our results show that the surface ferromagnetic phase exists in the weak random field range above the bulk critical temperature. The surface specific heat is not divergence and the susceptibility show a cusp singularity at the surface ferromagnetic-paramagnetic transition for a relatively large random field.

Surface phase diagrams of the spin-1 Ising model with a random surface field

Surface phase diagrams are investigated by means of the mean-field renormalization group method for Ising systems of spin-1 and spin- 1 2 ferromagnets with spin-1 surface layers. The tricritical point and reentrant phase transition of the surface magnetism are found.

Mean field renormalization group for the spin-1/2 XXZ model

The mean field renormalization group (MFRG) method is applied to the spin-1/2 XXZ model. The phase diagram is obtained for various lattice structures in two and three dimensions, as well as estimates for the critical exponents. The results of the original MFRG method are quite good, but the more sophisticated approach that also includes surface exponents is not suitable for application to the small clusters used here.

Fixed-scale transformation with allowance for short-range spin correlations

An improved form of the mean-field renormalization-group method is proposed. The improvement is achieved by the replacement by ordinary molecular field theory by an effective-field theory that takes into account spin correlations and by the use at the same time of a fixed-scale transformation for Ising clusters.

Non-equilibrium Ising model with competing Glauber dynamics

The authors consider a kinetic Ising model with ferromagnetic interactions that evolves in time according to two competing Glauber dynamics at different temperatures. The steady states of this non-equilibrium model are studied by using a dynamic pair approximation. When the temperatures are low enough the system orders in a ferromagnetic state, but if one of the temperatures is allowed to be negative the system may have an antiferromagnetic order. They obtain the phase diagram for the case of a square lattice. In this case they calculate the critical exponent v by using a mean field renormalization group method. The numerical results indicate that the model falls into the same universality class of the equilibrium Ising model. They also show that one particular case of the non-equilibrium model studied here is equivalent to the majority vote model.

Magnetic Phase Transitions in Quantum Ising Model with Annealed Antiferromagnetic Bond Randomness11The project supported by the Foundation of Doctoral Education.

The effect of annealed antiferromagnetic bond randomness on the phase transitions of the Quantum Ising Model (QIM) is studied by using mean-field renormalization group method. It is argued that bond randomness drastically alters multicritical phase diagram via transverse field. Multicritical points and coexistence region of ferromagnetic and antiferromagnetic case exist only at weak transverse field, and are entirely eliminated at strong transverse field. The coexistence region diminishes in reducing the fluctuation interaction. This physical picture demonstrates that the competition between transverse field and exchange interaction and fluctuation interaction via bond randomness play an important role in generating multiphase structure. Another consequence of competition is that tricritical points of first-second order phase transitions are not entirely eliminated by bond randomness in two-dimensional QIM.

STUDY OF SURFACE MAGNETISM IN A SEMI-INFINITE ISING FERROMAGNETIC SYSTEM

We use the mean field renormalization group method to treat the semi-infinite Ising ferromagnetic system with the amorphization of the surface. The critical behavior of the surface with a surface random field, including critical temperature, the possibility of tricritical and reentrant phenomena, are investigated in detail.

A mean-field renormalization group study of the finite temperature SU(2) lattice gauge theory at the strong coupling limit

Abstract The critical points and the critical indices of finite temperature SU (2) lattice gauge theory in the strong coupling limit have been calculated by using the mean-field renormalization group method. Results have been compared with the critical indices of the Ising spin system which are obtained by using the same method. The agreement between the results is in support of the Svetitsky-Yaffe conjecture.

Mean-field renormalization group with reaction field for diluted ising model

A mean-field renormalization group method including the reaction field is applied to diluted Ising systems. Two-dimensional bond dilution and both two- and three-dimensional site dilution are considered. For low and intermediate dilution, the phase diagrams agree well with other predictions, while for large dilution (near the percolation threshold) pathologies may show up related to the choice of the reaction field at low temperature.

Renormalization group treatment of a spin-one Ising model with biquadratic exchange interaction

The critical behavior of a spin-one Ising model with biquadratic exchange interactions is studied using the mean field renormalization group method. The phase diagram for various lattices is obtained. The nature of the phase transition with biquadratic interaction is analysed and comparison with other methods is made.

Mean field renormalization group analysis of the Blume-Capel model

The critical properties of the d -dimensional Blume-Capel model is studied by using the mean field renormalization group method. The phase diagram and tricritical behaviour of the square lattice and various three-dimensional lattices have been analysed. Results are compared with those of high-temperature series expansion and variational methods.