Mean-field Renormalization Group Research Articles

Improved mean-field-like renormalisation group approach for Z(q) symmetric spin models

Various modifications of the mean-field renormalisation group method are analysed to study the convergence of the critical coupling and critical exponents to their exact values as the cluster size increases. Appropriate choice of the length scaling factor or of the scaling quantity can give appreciable improvement over the conventional procedure for short clusters. The best values are achieved when both the bulk and surface critical behaviour are explicitly taken into account.

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.

Renormalisation group treatment of a random Potts model with different numbers of Potts spin states

The mean-field renormalisation group method is used to study a random Potts model which consists of a mixture of p-state and q-state Potts spins. The Hamiltonian is written in terms of a critical and a non-critical variable. The concentration dependence of the critical temperature and non-critical parameter is determined.

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.

Length scaling in MFRG

The mean-field renormalisation group (MFRG) has so far given poor estimates for critical indices. It is argued that this can be traced to an unsatisfactory definition of the length scaling factor. A new definition, that improves the estimates in most cases, is proposed.

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.

Mean-field renormalization group: Unified approach to bulk and surface critical behavior.

Mean-field renormalization group: Unified approach to bulk and surface critical behavior.

Mean field renormalization group study of surface effects in the Ising ferromagnet

We show that MFRG techniques provide a reasonable description of the critical behaviour of the semi-infinite three-dimensional Ising model, both in the pure and the diluted cases. Surface effects in percolation are obtained in the T → 0 limit of the diluted model, in agreement with previous work by De'Bell.

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.

Mean-field renormalisation group for the Potts model in a transverse field

The mean-field renormalisation group method is used to study the bond-diluted q-states Potts model in a transverse field. The critical surface in the transverse field-temperature-concentration space is obtained for different dimensionalities, and some critical exponents are estimated.

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.

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.

Two-step renormalisation group approach for randomly diluted Ising models

A two-step renormalisation group approach-a Migdal-Kadanoff (or decimation) transformation (MK) followed by a mean-field renormalisation group (MFRG)-has been applied to random bond Ising models on d-dimensional hypercubic lattices. Calculations of the critical couplings and percolation concentrations for two and three dimensions show much improvement, even for small size clusters, compared with the results of separate MK or MFRG calculations. Critical exponents nu T and nu p are also improved in some cases. Estimates of critical curves in the concentration-temperature plane are also obtained for the two- and three-dimensional models.

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.

Mean field renormalisation group calculations for directed percolation on the square lattice

A simple extrapolation technique for mean field renormalisation group calculations is described. Application of this method to large cell calculations for percolation on the directed square lattice yields pc=0.7067+or-0.0001 (site problem) and pc=0.6454+or-0.0002 (bond problem).

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.

Two-step renormalisation group for Ising systems

A decimation transformation preceded by a mean-field renormalisation group has been used to obtain the critical properties of various d-dimensional lattices. The method improves substantially both exponents and critical couplings even for small size clusters when compared with decimation and mean-field renormalisation group methods.

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.