Mean Field Renormalization Group Approach Research Articles

Diluted and random-bond Ising model for the Fe-Al disordered alloys.

A quenched disordered Ising model with a distribution function that includes dilution and random bonds is studied through the mean-field renormalization-group approach. Random bonds are considered through a ferromagnetic exchange interaction between nearest-neighbor spins (NN) and an antiferromagnetic exchange interaction between next-nearest-neighbor spins (NNN). The phase diagrams are obtained and the results are applied to Fe-Al disordered alloys.

Renormalization group study of the two-dimensional Ising model with crossing bonds

The simple quadratic Ising model with nearest- and next-nearest-neighbor interactions is investigated by means of the mean field renormalization group approach. By conveniently choosing the size of the blocks one obtains the expected phase diagram exhibiting ferromagnetic, antiferromagnetic, paramagnetic and superantiferromagnetic phases. The critical lines which separate the paramagnetic phase from the ordered ones have the expected asymptotic behavior for large values of the nearest-neighbor coupling.

Ising model on a semi-infinite lattice: mean field renormalization group approach

We determine the critical properties of the Ising model on a semi-infinite cubic lattice. We use the mean field renormalization group with clusters of up to 25 spins. We show that the critical surface coupling enhancement at the special transition is monotonic with increasing cluster size and goes towards the recent Monte Carlo calculations. We also show that this critical coupling decreases with the distance which the bulk is taken from the free surface, and we explain the high values found for it by real space renormalization group calculations.

Ising model in a transverse random field

The transverse random-field Ising model with a trimodal distribution is studied within mean-field and mean-field renormalization-group approaches. The phase diagram is obtained and all the transition lines are second order. An ordered phase persists for large random fields provided that the probability of the zero transverse field is greater than the site-percolation threshold.

Mean-field renormalization group approach to two-dimensional site directed percolation

Two-dimensional site directed percolation is studied by the mean-field renormalization group approach to bulk and surface critical properties. Extrapolation techniques for the exponents and the percolation threshold are described. A very good estimate of the percolation threshold (pc=0.7055+or-0.0001) and the first evaluation of the surface exponent yhs=0.653+or-1 are obtained.

Renormalization group study of the two-dimensional site-diluted Ising model

The quenched site-diluted Ising model on a two-dimensional square lattice is studied by employing the mean field renormalization group approach. The critical temperature as a function of the concentration is obtained and compared to other different types of approximation. Quite good results are achieved even by considering relatively small clusters.

Critical phenomena at surfaces in a model of nonequilibrium phase transitions

Critical phenomena at surfaces are studied in a simple two-dimensional model of non-equilibrium phase transitions belonging to the class of interacting particle systems. The mean field renormalization group approach and numerical simulations are used to determine the phase diagram for this system and some of the critical exponents associated with ordinary, special, extraordinary and surface phase transitions.

Ferromagnetic critical line of the Ising model with crossing bonds

The ferromagnetic critical line of the two-dimensional Ising model with nearest- and next-nearest-neighbor interactions is studied using the mean field renormalization group approach. The expected asymptotic behavior for large values of the nearest-neighbor interaction is achieved and the results are compared to those obtained from other methods.

Diluted and random-bond Ising model: Application to the Fe-Mn-Al alloys.

A quenched disordered Ising model with a distribution function that includes dilution and random bonds is studied through the mean-field renormalization-group approach. The phase diagram is obtained, and the results are applied to Fe-Mn-Al alloys. Fittings of the experimental phase diagram and the reduced mean hyperfine field at room temperature are shown to be better than those previously obtained through a single-site diluted model.

Double-Chain Mean-Field Renormalization Group Approach for the Ising Model11This work was supported by the Foundation of Doctor Education.

A double-chain mean-field renormalization group approach for the Ising model is formulated. With the approach, transition temperatures and critical exponents for several numbers of nearest-neighbor chains are obtained.

Field distributions and tricritical points in a random-field Ising model: Mean-field renormalization-group approach.

Field distributions and tricritical points in a random-field Ising model: Mean-field renormalization-group approach.

Mean field renormalization group for the spin- [formula omitted] random anisotropic Heisenberg model

The mean field renormalization group approach is applied to the spin- 1 2 random anisotropic Heisenberg mode. In this model the couplings between any pair of nearest-neighbour spins can be randomly isotropic (Heisenberg-like) or randomly anisotropic (Ising-like). The phase diagram and estimates of critical exponent are obtained for the two-and three-dimensional lattices.

Mean-field renormalisation group approach for the axial next-nearest-neighbour Ising model

The critical properties of the axial next-nearest-neighbour Ising (ANNNI) model are investigated by using the mean-field renormalisation group approach. Linear and double chain clusters lying along the axial direction are considered. Phase diagrams for the model in two and three dimensions and estimates of thermal exponents are obtained.

Renormalization group study of compressible Ising systems

The mean field renormalization group approach is used to study compressible Ising models. The phase diagram as well as estimates of critical exponents are obtained for systems where shear forces are neglected.

Mean-field renormalisation group study of the anisotropic Ising model

The mean-field renormalisation group approach is applied to the anisotropic Ising model by considering clusters consisting of finite blocks of spins and clusters consisting of infinite strips of spins with the finite widths. The critical temperature and estimates of the critical exponent nu are obtained as functions of the anisotropy. A two-step renormalisation group procedure using a phenomenological renormalisation transformation is also presented. In general, the results for nu are consistent with universality arguments.

Critical properties of the Ashkin-Teller model from the mean-field renormalisation group approach

By using small size clusters, which carry all the basic symmetries of the Ashkin-Teller model, the authors obtain within the mean-field renormalisation group approach the complete phase diagram of the model. Estimates of the thermal critical exponent are also obtained.

Diluted transverse Ising model within the mean field renormalization group

Clusters of different size and symmetry are exploited in the study of the diluted transverse Ising model on several lattices within the mean field renormalization group approach. It is noticed that the critical exponents depend both on the size of clusters as well as on the cluster symmetry. Harris' conjecture is verified for all lattices studied.

Quantum spin systems: dynamical mean field renormalisation group approach

The mean field renormalisation group approach is applied to the study of the static and dynamical critical properties of the spin-1/2 anisotropic Heisenberg model in a transverse field. The critical surface and estimates of static and dynamical critical exponents are obtained for the one-, two-, and three-dimensional models.

Mean field renormalisation group for the spin-1/2anisotropic Heisenberg model

The mean field renormalisation group approach is applied to the spin-1/2 anisotropic Heisenberg model. The critical temperature and the critical exponent are obtained as a function of the anisotropy for the two-dimensional model on square, triangular, and hexagonal lattices. The three-dimensional model on a simple cubic lattice is also analysed.

Mean field renormalisation group for the disordered transverse Ising model

The mean field renormalisation group approach is applied to the bond diluted transverse Ising model. The critical surface in the temperature-transverse field-concentration space is obtained for the two- and three-dimensional models and estimates of critical exponents are also presented.