New Type Of Effective-field Theory Research Articles

Subject index to volume 131

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 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.

A new effective field theory for the anisotropic Heisenberg ferromagnet

A new type of effective field theory (NEFT) is developed for the quantum spin system with anisotropic exchange interaction. The calculation is based on a two-atom cluster approximation, and effects from the rest spins are treated by the operator expansion technique assuming Ising character for surrounding spins. The Curie temperature Tc and spontaneous magnetization m are calculated for all Ising-, Heisenberg- and XY-like spin systems, and discussed comparing with results by other traditional pair spin theories. It is practically confirmed that Tc of the NEFT correctly reflects details of the geomtry of the lattice more than coordination number, and that it gives no anti-Curie point even for the XY-like spin system.

A NEW DISORDERED PHASE AND ITS PHYSICAL CONTENTS OF THE BLUME-EMERY-GRIFFITHS MODEL

Thermodynamic properties of the anisotropic Blume-Emery-Griffiths model are discussed in the new type of effective-field theory. A new disordered phase which may correspond to the staggered quadrupolar phase predicted by the Monte Carlo simulation is found and its physical contents are investigated.

New effective-field theory for the Blume-Capel model

A new type of effective-field theory that has recently been used with success for many applications concerning the usual two-state Ising model is herein extended to the Blume-Capel model. The method, which can explicitly and systematically include correlation effects, is illustrated in several lattice structures by employing its simplest approximate version, in which spin-spin correlations are neglected. It is shown that this approximative procedure, although analytically simple, provides in particular a vanishing critical temperature for one-dimensional systems and leads to results quite superior to those currently obtained within the Molecular Field Approximation for higher-dimensional systems. Within this framework we discuss as functions of temperature and for any values of the anisotropy parameter D, the order parameter, the thermal average of the square of the single-site spin variable, the internal energy and the specific heat as well as the ferromagnetic-phase stability limit. Whenever comparison is possible a satisfactory qualitative (and to a certain extent quantitative) agreement is observed with results available in the literature in which more sophisticated treatments are used. In particular, our result for the tricritical point at which the system exhibits a first-order phase transition is in quite good agreement with those obtained by using Series Expansion Methods.

The reaction fields for pure and dilute ising ferromagnets

The thermal behavior of the reaction field originally introduced by Onsager are investigated for the pure and diluted Ising ferromagnetic square lattices in terms of a new type of effective-field theory with correlations. We find that in contrast with the case of a pure magnet the concept of reaction field becomes important for the description of a disordered magnet.

Amorphization of a quasi-one-dimensional Ising ferromagnet

The amorphization of a quasi-one-dimensional Ising ferromagnet is investigated with the use of a new type of effective-field theory with correlations. The exchange parameters of interchain and intrachain interactions are assumed to have $\ensuremath{\delta}$-function distributions. We find some characteristic behavior for the amorphization.

Amorphization of a crystalline diluted Ising ferromagnet: Studies of its high-field magnetization

The high-field magnetization for the amorphization of a diluted Ising ferromagnet in a square lattice is investigated by means of a new type of effective-field theory with correlations. The exchange parameters are assumed to have a $\ensuremath{\delta}$-function distribution. We study behavior characteristic of the high-field-magnetization case, in particular, the temperature dependence of the magnetization (especially for systems showing reentrant phenomenon), the magnetization versus inverse field, and we construct Arrott plots.

Amorphization of a crystalline diluted Ising ferromagnet

The amorphization of a diluted Ising ferromagnet on a square lattice is investigated with the use of a new type of effective-field theory with correlation. The exchange parameters are assumed to be distributed according to a $\ensuremath{\delta}$ function. The transition temperature, phase diagram, magnetization, and susceptibility are evaluated. We find some characteristic behavior for the amorphization.

New effective-field theory for the Potts model

A new type of effective-field theory that has recently been used with success for many applications concerning the Ising model is, through the generalization of Callen identities, herein extended to the $q$-state Potts model. Although mathematically simple, it yields results quite superior to those currently obtained within the molecular-field approximation. In order to test its reliability we check the following properties: (a) The critical temperature ${T}_{c}$ associated with a linear chain vanishes for all $q$, (b) the value of ${T}_{c}$ associated with a $z$-fold-coordinated lattice ($z>2$) exhibits a qualitatively (and, to a certain extent, quantitatively) satisfactory $q$ dependence, (c) the $z\ensuremath{\rightarrow}\ensuremath{\infty}$ limit reproduces the exact value for ${T}_{c}$, and (d) for fixed $z$, all values of $q>2$ provide first-order phase transitions, which are exact for $d>4$. Furthermore, the procedures for obtaining, as functions of temperature and for any values of $q$ and $z$, the order parameter, internal energy, and specific heat are outlined, and some typical illustrations are presented.

Surface magnetic properties of the Ising model with a diluted free surface

A semi-infinite ferromagnetic simple cubic Ising lattice which has nonmagnetic impurities substituted for the magnetic species only at the surface is investigated with the use of a new type of effective-field theory with correlation. The surface magnetism is examined as a function of modified exchange ${J}_{s}=J(1+\ensuremath{\Delta})$ and concentration $P$ of magnetic atoms at the surface. The critical value ${\ensuremath{\Delta}}_{c}$, transition temperatures ${T}_{c}^{s}$, and phase diagram for surface ordering are obtained as functions of $P$ and $\ensuremath{\Delta}$. The reduced magnetization curves of surface and bulk are also studied. We obtain some characteristic behaviors of magnetism at the diluted surface.

Contribution to the new type of effective-field theory of the Ising model

A new type of effective-field theory of the Ising model is presented. The differential-operator method is introduced into the exact spin correlation function identity obtained by Callen. The Curie temperatures are evaluated by using two different types of effective Hamiltonians. It is also shown how the Zernike and the Bethe-Peierls equations can be reproduced within one framework depending on the choice of effective fields in an effective Hamiltonian. The spin correlation function and the specific heat are presented.