Type Of Effective-field Theory Research Articles

Effective field theory with differential operator technique for dynamic phase transition in ferromagnetic Ising model

The non-equilibrium phase transition in a ferromagnetic Ising model is investigated by use of a new type of effective field theory (EFT) which correctly accounts for all the single-site kinematic relations by differential operator technique. In the presence of a time dependent oscillating external field, with decrease of the temperature the system undergoes a dynamic phase transition, which is characterized by the period averaged magnetization Q, from a dynamically disordered state Q = 0 to the dynamically ordered state Q ≠ 0. The results of the dynamic phase transition point Tc determined from the behavior of the dynamic magnetization and the Liapunov exponent provided by EFT are improved than that of the standard mean field theory (MFT), especially for the one dimensional lattice where the standard MFT gives incorrect result of Tc = 0 even in the case of zero external field.

Dimensional crossover behaviour of the zero-temperature magnetization for the selective magnetic dilution

By a new type of effective field theory we have studied a selective magnetic dilution for the Ising ferromagnet having various sublattice structures. In the concentration dependence of the zero-temperature magnetization, we found an interesting dimensional crossover behaviour characteristic of the case of extreme site selectivity.

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.

Constraints on black hole remnants.

One possible fate of information lost to black holes is its preservation in black hole remnants. It is argued that a type of effective field theory describes such remnants (generically referred to as informons). The general structure of such a theory is investigated and the infinite pair production problem is revisited. A toy model for remnants clarifies some of the basic issues; in particular, infinite remnant production is not suppressed simply by the large internal volumes as proposed in cornucopion scenarios. Criteria for avoiding infinite production are stated in terms of couplings in the effective theory. Such instabilities remain a problem barring what would be described in that theory as a strong coupling conspiracy. The relation to euclidean calculations of cornucopion production is sketched, and potential flaws in that analysis are outlined. However, it is quite plausible that pair production of ordinary black holes (e.g. Reissner Nordstrom or others) is suppressed due to strong effective couplings. It also remains an open possibility that a microscopic dynamics can be found yielding an appropriate strongly coupled effective theory of neutral informons without infinite pair production.

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.

A New Effective Field Theory for Dilute Ising Ferromagnets

AbstractA new type of effective field theory for a quenched site diluted Ising model is presented. As a result the general equation for magnetization is obtained. Particular emphasis is given to the honeycomb lattice for which the critical concentration and concentration dependence of the magnetization and critical temperature are calculated. The critical concentrations for a square and simple cubic lattice are also obtained.

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.

A New Type of Effective Field Theory for Ising Model with Spin −1/2

A New Type of Effective Field Theory for Ising Model with Spin −1/2

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.