I.P. Fittipaldi

Thermodynamical properties of the transverse Ising model

A new effective field theory is proposed and used to derive the thermodynamical properties of the transverse Ising model. The formalism is based on an exact formal spin identity for the two-state transverse Ising model and utilizes an exponential operator technique. The method, which can explicitly and systematically include correlation effects, is illustrated in several lattice structures by employing its simplest approximation version (in which spin-spin correlations are neglected). The lines of critical points in the Ω-T plane as well as the thermal behaviour of both transverse and longitudinal magnetizations are analysed for square and simple cubic lattices. It is shown that the present formalism, in spite of its simplicity, yields results which represent a remarkable improvement on the standard mean field treatment (MFA).

Thermodynamical properties of a mixed Ising ferromagnet system

Abstract The critical behavior of a mixed ferromagnetic Ising spin system consisting of spin −1 2 and spin −1, with a single-ion uniaxial crystal field included, is studied by the use of a newly developed effective-field theory. The nature of the phase diagram is analysed for square and honeycomb lattices and comparison with a special exact solution and other approximation schemes are made.

Effective field renormalization group approach for Ising lattice spin systems

Abstract A new applicable real-space renormalization group framework (EFRG) for computing the critical properties of Ising lattice spin systems is presented. The method, which follows up the same strategy of the mean-field renormalization group scheme (MFRG), is based on rigorous Ising spin identities and utilizes a convenient differential operator expansion technique. Within this scheme, in contrast with the usual mean-field type of equation of state, all the relevant self-spin correlations are taken exactly into account. The results for the critical coupling and the critical exponent v , for the correlation length, are very satisfactory and it is shown that this technique leads to rather accurate results which represent a remarkable improvement on those obtained from the standard MFRG method. In particular, it is shown that the present EFRG approach correctly distinguishes the geometry of the lattice structure even when employing its simplest size-cluster version. Owing to its simplicity we also comment on the wide applicability of the present method to problems in crystalline and disordered Ising spin systems.

A unified effective‐field renormalization‐group framework approach for the quenched diluted Ising models

A unified effective‐field renormalization‐group framework (EFRG) for both quenched bond‐ and site‐diluted Ising models is herein developed by extending recent works. The method, as in the previous works, follows up the same strategy of the mean‐field renormalization‐group scheme (MFRG), and is achieved by introducing an alternative way for constructing classical effective‐field equations of state, based on rigorous Ising spin identities. The concentration dependence of the critical temperature, Tc(p), and the critical concentrations of magnetic atoms, pc, at which the transition temperature goes to zero, are evaluated for several two‐ and three‐dimensional lattice structures. The obtained values of Tc and pc and the resulting phase diagrams for both bond and site cases are much more accurate than those estimated by the standard MFRG approach. Although preserving the same level of simplicity as the MFRG, it is shown that the present EFRG method, even by considering its simplest size‐cluster version, provid...

Phase diagrams of the spin-one transverse Ising model

Abstract An effective field theory is proposed and used to derive the phase diagrams of the spin-1 Ising model in the presence of an applied transverse field. The lines of critical points in the T−Ω plane are analyzed for several lattice structures and compared with the standard mean field (MFA) predictions. The spin-1 phase boundary line is also compared with that of spin- 1 2 for the honeycomb lattice. In spite of its simplicity, the present formalism yields results which represent a remarkable improvement on the usual MFA treatment.

Tricritical behavior of a mixed ising spin system within the effective-field approximation

Abstract We investigate the ability of the effective-field theory, within the one- and two-spin cluster approximation, to predict the absence of tricritical behavior, for a mixed spin- 1 2 and spin-1 Ising system on the honeycomb and the square lattice.

Thermodynamical properties of the spin-one transverse Ising model

A new type of effective-field theory that has recently been used with success for many applications concerning the two-state transverse Ising model (spin-12 TIM), is herein extended to the spin-1 TIM. The method, which can explicitly and systematically include correlation effects, is illustrated by employing its simplest approximation version, in which multispin correlations are neglected. The lines of critical points in the T-Ω plane as well as the thermal behavior of all relevant statistical-mechanical quantities are analysed for several lattice structures and compared with the standard mean-field predictions. It is shown that the present formalism, in spite of its simplicity, yields results quite superior to those currently obtained within the molecular-field approximation.

Thermodynamical properties of a Heisenberg model with Dzyaloshinski–Moriya interactions

Within the framework of a new correlated effective‐field theory (CEF) the effects of the Dzyaloshinski–Moriya (DM) interactions on magnetic properties of the spin‐1/2 anisotropicHeisenberg model are discussed. The CEF theory is based on a generalized but approximate Callen–Suzuki spin relation for cluster with two spins, and makes use of the Honmura–Kaneyoshi exponential operator technique. The phase diagram and the thermal behavior of magnetization are analyzed for the simple cubic lattice, and compared with the corresponding two‐spin cluster mean‐field (MFA) predictions. It is shown that for the easy direction (D=D z; where D is the DM vector coupling), the model exhibit a tricritical point (TCP), at which the phase transition changes from second to first order. The TCP is explicitly obtained, and the tricritical temperature, T t , is independent of the exchange anisotropy parameter Δ (Δ=0 and Δ=1, correspond the isotropic Heisenberg and Ising models, respectively), while the tricritical parameter, D t , has dependence on Δ. In spite of its simplicity, the present CEF formalism yields results, which represent a remarkable improvement on the usual MFA treatment.

Phase diagrams for the bond- and site-diluted transverse Ising model☆

A unified effective-field treatment for both quenched bond- and site-diluted transverse Ising models is presented. The method which can explicitly and systematically include correlation effects, is applied to several Z-fold-coordinated lattices (Z = 3, 4 and 6) in its simplest approximate version. Although mathematically simple, it yields results quite superior to those currently obtained within the standard molecular-field treatments. Whenever comparison is possible a satisfactory qualitative (and to a certain extent quantitative) agreement is observed with results available in the literature. A particular emphasis is given to the honeycomb lattice for which no unified treatment has been done.

Critical behavior of the anisotropic Heisenberg model by effective‐field renormalization group

A real‐space effective‐field renormalization‐group method (ERFG) recently derived for computing critical properties of Ising spins is extended to treat the quantum spin‐1/2 anisotropic Heisenberg model. The formalism is based on a generalized but approximate Callen–Suzuki spin relation and utilizes a convenient differential operator expansion technique. The method is illustrated in several lattice structures by employing its simplest approximation version in which clusters with one (N’=1) and two (N=2) spins are used. The results are compared with those obtained from the standard mean‐field (MFRG) and Migdal–Kadanoff (MKRG) renormalization‐group treatments and it is shown that this technique leads to rather accurate results. It is shown that, in contrast with the MFRG and MKRG predictions, the EFRG, besides correctly distinguishing the geometries of different lattice structures, also provides a vanishing critical temperature for all two‐dimensional lattices in the isotropic Heisenberg limit. For the simpl...