Multi-Critical Dynamics for the +/- J Ising Model

We perform the exact TDRG transformations on the kinetic Ising model of the braced ladder whose R min is 5. Within our knowledge, this is the only example that the exact TDRG transformations have been performed on a system with R min > 2. We show that under Achiam's linear response theory there must be important excitations of the multi-spin operators in the kinetic Ising models of the systems with R min > 2, the dynamic critical behaviours of the systems are greatly affected by these excitations. Moreover, we get the conclusion that for the kinetic Ising models of the systems with R min = ∞ exact TDRG calculations are impossible. The complete new and interesting results are given.We perform the exact TDRG transformations on the kinetic Ising model of the braced ladder whose R min is 5. Within our knowledge, this is the only example that the exact TDRG transformations have been performed on a system with R min > 2. We show that under Achiam's linear response theory there must be important excitations of the multi-spin operators in the kinetic Ising models of the systems with R min > 2, the dynamic critical behaviours of the systems are greatly affected by these excitations. Moreover, we get the conclusion that for the kinetic Ising models of the systems with R min = ∞ exact TDRG calculations are impossible. The complete new and interesting results are given.

Acta Physica Sinica (Overseas Edition)Dec 1, 19930 citations

Critical dynamics of finite Ising model

Jean Christian Anglès d’Auriac, R. Maynard, R. Rammal

Journal of Statistical PhysicsJun 1, 198227 citations

HIGH SPEED ALGORITHMS AND SIMULATIONS OF THE CRITICAL DYNAMICS OF THE ISING MODEL

Hans-Otto Heuer

We review the development of Monte Carlo algorithms for the simulation of the Ising model with local dynamics. The multi lattice coding algorithm for the pure and for the site-disordered Ising model is described in detail. Application of these algorithms on fast vector computers have led to new progress concerning the critical dynamics of the pure Ising model leading to the critical exponent z = 2:05. The importance of disorder for the critical dynamics of the Ising model has been investigated recently. We review the numerical results and compare with theoretical predictions. A crossover scenario is found as for the static behavior with an effective dynamical exponent z = 1:75 fl. 1 Introduction The Ising model is a standard model in statistical physics for the description of a ferromagnet in an extremely simplified manner. It is assumed that quantum spin operators may be replaced by classical spins S i = \\Sigma 1 which are oriented parallel or antiparallel to a magnetic filed H: H...We review the development of Monte Carlo algorithms for the simulation of the Ising model with local dynamics. The multi lattice coding algorithm for the pure and for the site-disordered Ising model is described in detail. Application of these algorithms on fast vector computers have led to new progress concerning the critical dynamics of the pure Ising model leading to the critical exponent z = 2:05. The importance of disorder for the critical dynamics of the Ising model has been investigated recently. We review the numerical results and compare with theoretical predictions. A crossover scenario is found as for the static behavior with an effective dynamical exponent z = 1:75 fl. 1 Introduction The Ising model is a standard model in statistical physics for the description of a ferromagnet in an extremely simplified manner. It is assumed that quantum spin operators may be replaced by classical spins S i = \\Sigma 1 which are oriented parallel or antiparallel to a magnetic filed H: H...

WORLD SCIENTIFIC eBooksMay 1, 19961 citation

Critical Dynamics in Simple Ising-Like Systems

Gene F. Mazenko

Springer series in solid-state sciencesJan 1, 19830 citations

Ising ferromagnets in Ising-percolation square lattices, an example of Ising-Ising coupling

Jafar Cheraghalizadeh, M. N. Najafi

In this paper we consider the Ising model (called the dynamical Ising model with dynamical temperature $T$ ) on the Ising-correlated percolation lattice. To construct this lattice, another Ising model (which is called the quenched Ising model with quench artificial temperature ${T}_{q}$ ) is employed to model the correlations between imperfections. We argue that for each quenched temperature, there is a particular dynamical temperature ${T}_{c}({T}_{q})$ for which the dynamical Ising model becomes critical. We present some finite-size arguments (based on the moments of the magnetism and the energy as well as the spanning cluster probability) to extract the critical points and also show that they are compatible with the finite-size scaling of the singular point of the magnetic susceptibility. The model is thoroughly characterized in and out of these points. We find that the critical behaviors of the model change significantly with respect to the regular Ising model as well as the Ising model on the uncorrelated percolation lattice. It is shown that for the critical lattice, ${T}_{q}={T}_{c}^{\text{square}\phantom{\rule{4.pt}{0ex}}\text{Ising}\phantom{\rule{4.pt}{0ex}}\text{model}}\ensuremath{\approx}2.269$, the critical temperature for the dynamical Ising model in the thermodynamic limit is ${T}_{c}({T}_{q}={T}_{c}^{\text{square}\phantom{\rule{4.pt}{0ex}}\text{Ising}\phantom{\rule{4.pt}{0ex}}\text{model}})=1.94\ifmmode\pm\else\textpm\fi{}0.005$, and the fractal dimension of the exterior perimeter of geometrical spin clusters is ${D}_{f}^{T={T}_{c}({T}_{q}=2.269)}=1.408\ifmmode\pm\else\textpm\fi{}0.002$. Many quantities, such as the dynamical critical temperatures, all local and global critical exponents, and the fractal dimension of loops ${D}_{f}$ , scale with the quench temperature in a power-law fashion, with some critical exponents that are reported. Significantly we see that ${D}_{f}^{T={T}_{c}({T}_{q})}\ensuremath{-}{D}_{f}^{T={T}_{c}({T}_{q}=2.269)}\ensuremath{\sim}\frac{1}{\sqrt{\ensuremath{\zeta}({T}_{q})}}$ in which $\ensuremath{\zeta}({T}_{q})$ is the correlation length of the quenched Ising model at temperature ${T}_{q}$ .In this paper we consider the Ising model (called the dynamical Ising model with dynamical temperature $T$) on the Ising-correlated percolation lattice. To construct this lattice, another Ising model (which is called the quenched Ising model with quench artificial temperature ${T}_{q}$) is employed to model the correlations between imperfections. We argue that for each quenched temperature, there is a particular dynamical temperature ${T}_{c}({T}_{q})$ for which the dynamical Ising model becomes critical. We present some finite-size arguments (based on the moments of the magnetism and the energy as well as the spanning cluster probability) to extract the critical points and also show that they are compatible with the finite-size scaling of the singular point of the magnetic susceptibility. The model is thoroughly characterized in and out of these points. We find that the critical behaviors of the model change significantly with respect to the regular Ising model as well as the Ising model on the uncorrelated percolation lattice. It is shown that for the critical lattice, ${T}_{q}={T}_{c}^{\text{square}\phantom{\rule{4.pt}{0ex}}\text{Ising}\phantom{\rule{4.pt}{0ex}}\text{model}}\ensuremath{\approx}2.269$, the critical temperature for the dynamical Ising model in the thermodynamic limit is ${T}_{c}({T}_{q}={T}_{c}^{\text{square}\phantom{\rule{4.pt}{0ex}}\text{Ising}\phantom{\rule{4.pt}{0ex}}\text{model}})=1.94\ifmmode\pm\else\textpm\fi{}0.005$, and the fractal dimension of the exterior perimeter of geometrical spin clusters is ${D}_{f}^{T={T}_{c}({T}_{q}=2.269)}=1.408\ifmmode\pm\else\textpm\fi{}0.002$. Many quantities, such as the dynamical critical temperatures, all local and global critical exponents, and the fractal dimension of loops ${D}_{f}$, scale with the quench temperature in a power-law fashion, with some critical exponents that are reported. Significantly we see that ${D}_{f}^{T={T}_{c}({T}_{q})}\ensuremath{-}{D}_{f}^{T={T}_{c}({T}_{q}=2.269)}\ensuremath{\sim}\frac{1}{\sqrt{\ensuremath{\zeta}({T}_{q})}}$ in which $\ensuremath{\zeta}({T}_{q})$ is the correlation length of the quenched Ising model at temperature ${T}_{q}$.

Physical review. ENov 26, 20184 citations

In this paper we consider the Ising model (called the dynamical Ising model with dynamical temperature

T

) on the Ising-correlated percolation lattice. To construct this lattice, another Ising model (which is called the quenched Ising model with quench artificial temperature

{T}_{q}

) is employed to model the correlations between imperfections. We argue that for each quenched temperature, there is a particular dynamical temperature

{T}_{c}({T}_{q})

for which the dynamical Ising model becomes critical. We present some finite-size arguments (based on the moments of the magnetism and the energy as well as the spanning cluster probability) to extract the critical points and also show that they are compatible with the finite-size scaling of the singular point of the magnetic susceptibility. The model is thoroughly characterized in and out of these points. We find that the critical behaviors of the model change significantly with respect to the regular Ising model as well as the Ising model on the uncorrelated percolation lattice. It is shown that for the critical lattice, ${T}_{q}={T}_{c}^{\text{square}\phantom{\rule{4.pt}{0ex}}\text{Ising}\phantom{\rule{4.pt}{0ex}}\text{model}}\ensuremath{\approx}2.269$, the critical temperature for the dynamical Ising model in the thermodynamic limit is ${T}_{c}({T}_{q}={T}_{c}^{\text{square}\phantom{\rule{4.pt}{0ex}}\text{Ising}\phantom{\rule{4.pt}{0ex}}\text{model}})=1.94\ifmmode\pm\else\textpm\fi{}0.005$, and the fractal dimension of the exterior perimeter of geometrical spin clusters is ${D}_{f}^{T={T}_{c}({T}_{q}=2.269)}=1.408\ifmmode\pm\else\textpm\fi{}0.002$. Many quantities, such as the dynamical critical temperatures, all local and global critical exponents, and the fractal dimension of loops

{D}_{f}

, scale with the quench temperature in a power-law fashion, with some critical exponents that are reported. Significantly we see that ${D}_{f}^{T={T}_{c}({T}_{q})}\ensuremath{-}{D}_{f}^{T={T}_{c}({T}_{q}=2.269)}\ensuremath{\sim}\frac{1}{\sqrt{\ensuremath{\zeta}({T}_{q})}}$ in which $\ensuremath{\zeta}({T}_{q})$ is the correlation length of the quenched Ising model at temperature

{T}_{q}