physica status solidi (b)

Extended linear chain approximation to the anisotropic ferromagnetic ising model

J. R. Faleiro Ferreira, N. P. Silva

Published Nov 1, 1982• 10 citations

Abstract

Abstract Approximate critical temperatures of anisotropic ferromagnetic Ising models are calculated through a recently proposed extended variational method in statistical mechanics. Using a linear chain Ising Hamiltonian in an effective field as trial Hamiltonian, quite good results are obtained.

DOI: 10.1002/pssb.2221140105

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Investigation of Oguchi's procedure applied to the ising model

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physica status solidi (b)

Extended linear chain approximation to the anisotropic ferromagnetic ising model

J. R. Faleiro Ferreira, N. P. Silva

Published Nov 1, 1982• 10 citations

Publisher

Abstract

DOI: 10.1002/pssb.2221140105

Related papers

Investigation of Oguchi's procedure applied to the ising model

J. R. Faleiro Ferreira, N. P. Silva

physica status solidi (b)Mar 1, 19836 citations

Correlated-effective-field treatment of the anisotropic Ising ferromagnet: Thermodynamical properties

R. Honmura

Within a new type of correlated-effective-field theory we calculate the effective-field parameters (including their response to external field), critical temperatures, susceptibility, short-range order parameters, and specific heat associated with an anisotropic, square-lattice, spin-\textonehalf{} Ising ferromagnet. The present formalism, which is shown to recover the Bethe-Peierls thermodynamics for the pure $Z$ -coordinated-lattice, spin-\textonehalf{} Ising model, yields satisfactory results; in particular, the crossover from a pure Ising ferromagnet on a square lattice to that on a linear chain is reasonably exhibited in the behavior of the susceptibility and the specific heat.Within a new type of correlated-effective-field theory we calculate the effective-field parameters (including their response to external field), critical temperatures, susceptibility, short-range order parameters, and specific heat associated with an anisotropic, square-lattice, spin-\textonehalf{} Ising ferromagnet. The present formalism, which is shown to recover the Bethe-Peierls thermodynamics for the pure $Z$-coordinated-lattice, spin-\textonehalf{} Ising model, yields satisfactory results; in particular, the crossover from a pure Ising ferromagnet on a square lattice to that on a linear chain is reasonably exhibited in the behavior of the susceptibility and the specific heat.

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Anisotropic Ising model in a magnetic field: Effective-field theory analysis

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Physical Review BJun 23, 200632 citations

Critical Temperature of a Quasi‐One‐Dimensional Ising Model. The Bethe‐Peierls Approximation

M. A. Yurishchev

physica status solidi (b)Apr 1, 19855 citations

A variational approach for the free energy

J. R. Faleiro Ferreira, N P Silva

To calculate thermodynamic functions in statistical mechanics the authors propose a new variational approach which has as particular cases the approaches of Bogoliubov, Oguchi and Tsallis-da Silva (1982), but introduces some improvements, mainly in the short-range order effects above the critical temperature. It requires a choice of a trial Hamiltonian that defines an approximate ensemble through which the thermodynamic functions may be calculated. To check the efficiency of their approach they apply it to the ferromagnetic Ising model by using the simplest possible trial Hamiltonian.To calculate thermodynamic functions in statistical mechanics the authors propose a new variational approach which has as particular cases the approaches of Bogoliubov, Oguchi and Tsallis-da Silva (1982), but introduces some improvements, mainly in the short-range order effects above the critical temperature. It requires a choice of a trial Hamiltonian that defines an approximate ensemble through which the thermodynamic functions may be calculated. To check the efficiency of their approach they apply it to the ferromagnetic Ising model by using the simplest possible trial Hamiltonian.

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A Variational Linear Approach for the Free Energy Applied to the Ising Model

J. R. Faleiro Ferreira

physica status solidi (b)Aug 1, 19886 citations

Z

-coordinated-lattice, spin-\textonehalf{} Ising model, yields satisfactory results; in particular, the crossover from a pure Ising ferromagnet on a square lattice to that on a linear chain is reasonably exhibited in the behavior of the susceptibility and the specific heat.

({J}_{x})

in the

x

direction and antiferromagnetic interaction

({J}_{y})

in the

y

direction. The phase diagram in the $T\text{\ensuremath{-}}H$ plane is obtained for the particular case

{J}_{x}={J}_{y}

. Special focus is given in the low-temperature region of the phase diagram, where a first-order phase transition is observed using the mean-field approximation, which is in disagreement with the linear chain approximation (LCA). Our results indicate a second-order phase transition for all values of

H∕J∊[0,2]

, with the presence of a reentrant behavior only observed in the BP approximation in accordance with the results of the LCA and exact solution. The null field critical temperature is an increasing function of

r={J}_{y}∕{J}_{x}

, and in the $r\ensuremath{\rightarrow}0$ limit we have found, using BP and EFT, the approximate form ${k}_{B}{T}_{N}∕{J}_{x}\ensuremath{\simeq}A∕\mathrm{ln}(1∕r)$ in accordance with the exact result of Onsager.