A new approach towards the critical properties of the Ising model

The critical properties of random ferromagnets with pure specific-heat exponent ${\ensuremath{\alpha}}_{P}=0$ are analyzed using renormalization-group methods. The origin and form of the impurity-induced logarithmic corrections for the random two-dimensional Ising model are discussed. Corrections develop only for the specific heat, which presents a new singularity of the form ${|\mathrm{ln}|T\ensuremath{-}{T}_{c}||}^{1\ensuremath{-}\ensuremath{\mu}}$ as well as a new critical exponent $\ensuremath{\mu}$.The critical properties of random ferromagnets with pure specific-heat exponent ${\ensuremath{\alpha}}_{P}=0$ are analyzed using renormalization-group methods. The origin and form of the impurity-induced logarithmic corrections for the random two-dimensional Ising model are discussed. Corrections develop only for the specific heat, which presents a new singularity of the form ${|\mathrm{ln}|T\ensuremath{-}{T}_{c}||}^{1\ensuremath{-}\ensuremath{\mu}}$ as well as a new critical exponent $\ensuremath{\mu}$.

Physical review. B, Condensed matterApr 1, 198319 citations

Critical behaviour of the Ising model

J. Hubbard

Physics Letters AJun 1, 197273 citations

Dynamics of the Ising Model near the Critical Point

Masuo Suzuki, 英雄猪狩

Jul 20, 19680 citations

New real-space renormalization techniques and their application to models of various spin and space dimensionalities

Wolfgang Kinzel

The mean-field approximation is used for the evaluation of the Niemeijer---Van Leeuwen real-space renormalization. Although this new method is very simple, it gives reasonable results for the critical properties of two-, three-, and four-dimensional Ising models, for the transition temperature ${T}_{c}$ of an Ising model with clusters and for the two-dimensional Ising antiferromagnet in an external magnetic field. Using this new mean-field renormalization in connection with the real-space renormalization of the kinetic Ising model, which recently has been suggested by the author, we obtain the long-time relaxation of the magnetization for all temperatures above ${T}_{c}$ . In the last application the critical properties of $n$ -dimensional spins in two and three space dimensions are calculated for arbitrary $n$ . Here the mean-field approximation and Monte Carlo methods are used to evaluate the renormalization step.The mean-field approximation is used for the evaluation of the Niemeijer---Van Leeuwen real-space renormalization. Although this new method is very simple, it gives reasonable results for the critical properties of two-, three-, and four-dimensional Ising models, for the transition temperature ${T}_{c}$ of an Ising model with clusters and for the two-dimensional Ising antiferromagnet in an external magnetic field. Using this new mean-field renormalization in connection with the real-space renormalization of the kinetic Ising model, which recently has been suggested by the author, we obtain the long-time relaxation of the magnetization for all temperatures above ${T}_{c}$. In the last application the critical properties of $n$-dimensional spins in two and three space dimensions are calculated for arbitrary $n$. Here the mean-field approximation and Monte Carlo methods are used to evaluate the renormalization step.

Physical review. B, Condensed matterMay 1, 197923 citations

On the critical dynamics of one-dimensional Ising models

Michel Droz, J. Kamphorst Leal da Silva, Anna‐Sapfo Malaspinas

Physics Letters AMay 1, 198649 citations

New effective field theory for the transverse Ising model

F. C. Sá Barreto, I. P. Fittipaldi, Boštjan Žekš

A new type effective field approach is used to derive the thermodynamical properties of the transverse Ising model. The method is based on an exact formal identity for the two-state transverse Ising model and utilizes an exponential operator technique. The lines of critical points in the Ω-T plane are derived and the critical transverse fields ΩC are obtained analytically, for lattices with coordination numbers z = 2, 4 and 6. This simple method yields results which represent a remarkable improvement on the usual mean field approximation. Our results are also compared with those from series expansion method.A new type effective field approach is used to derive the thermodynamical properties of the transverse Ising model. The method is based on an exact formal identity for the two-state transverse Ising model and utilizes an exponential operator technique. The lines of critical points in the Ω-T plane are derived and the critical transverse fields ΩC are obtained analytically, for lattices with coordination numbers z = 2, 4 and 6. This simple method yields results which represent a remarkable improvement on the usual mean field approximation. Our results are also compared with those from series expansion method.

FerroelectricsOct 1, 1981196 citations

{T}_{c}

of an Ising model with clusters and for the two-dimensional Ising antiferromagnet in an external magnetic field. Using this new mean-field renormalization in connection with the real-space renormalization of the kinetic Ising model, which recently has been suggested by the author, we obtain the long-time relaxation of the magnetization for all temperatures above

{T}_{c}

. In the last application the critical properties of

n

-dimensional spins in two and three space dimensions are calculated for arbitrary

n

. Here the mean-field approximation and Monte Carlo methods are used to evaluate the renormalization step.