The critical exponents at the glass temperature ${T}_{g}$ of a spin glass are estimated by making use of predictions obtained from a phase-space percolation model, in combination with scaling arguments. With this hypothesis, the whole set of exponents for a given system, including the dynamic exponent, can be expressed simply in terms of a single nonuniversal parameter. The model is checked against data from simulations and from three sets of experiments; agreement is very satisfactory.The critical exponents at the glass temperature ${T}_{g}$ of a spin glass are estimated by making use of predictions obtained from a phase-space percolation model, in combination with scaling arguments. With this hypothesis, the whole set of exponents for a given system, including the dynamic exponent, can be expressed simply in terms of a single nonuniversal parameter. The model is checked against data from simulations and from three sets of experiments; agreement is very satisfactory.

Physical review. B, Condensed matterJun 1, 198836 citations

Critical Exponents of the Three-Dimensional Ising Spin Glass

H.G. Ballesteros, Andrés De la Cruz, L. A. Fernández +7 more

Jun 13, 20000 citations

Critical behaviour of the two-dimensional EA model with a Gaussian bond distribution

Naoki Kawashima, Naomichi Hatano, Masuo Suzuki

The spin-glass susceptibility of the two-dimensional EA model is investigated by the numerical transfer-matrix method. It is found that the droplet picture gives a fairly good description of the critical behaviour. The critical exponent theta identical to -1/ nu is estimated as theta =-0.48(1), both through finite-size scaling and through the coherent-anomaly method (CAM). The present estimate is consistent with the authors' previous estimate theta =-0.476. These values do not, however, agree with the stiffness-exponent estimate theta S through the domain-wall scaling. This disagreement suggests that the assumption theta = theta S in the domain-wall scaling does not hold.The spin-glass susceptibility of the two-dimensional EA model is investigated by the numerical transfer-matrix method. It is found that the droplet picture gives a fairly good description of the critical behaviour. The critical exponent theta identical to -1/ nu is estimated as theta =-0.48(1), both through finite-size scaling and through the coherent-anomaly method (CAM). The present estimate is consistent with the authors' previous estimate theta =-0.476. These values do not, however, agree with the stiffness-exponent estimate theta S through the domain-wall scaling. This disagreement suggests that the assumption theta = theta S in the domain-wall scaling does not hold.

Journal of Physics A Mathematical and GeneralOct 7, 199230 citations

Percolation Theory of Phase Transitions in Spin Models

Chin‐Kun Hu

Chinese Journal of PhysicsAug 1, 19841 citation

On the critical dynamics of spin-glasses

Vladimir V. Prudnikov, G. B. Teǐtel'Baum

Physics Letters AMar 1, 19771 citation

Coherent Anomaly Method Calculationon the Cluster Variation Method. II.Critical Exponents of Bond Percolation Model

Koh Wada, Naotosi Watanabe, Tetsuya Uchida

The critical exponents of the bond percolation model are calculated in the D (=2, 3,···)-dimensional simple cubic lattice on the basis of Suzuki's coherent anomaly method (CAM) by making use of a series of the pair, the square-cactus and the square approximations of the cluster variation method (CVM) in the s -state Potts model. These simple approximations give reasonable values of critical exponents α, β, γ and ν in comparison with ones estimated by other methods. It is also shown that the results of the pair and the square-cactus approximations can be derived as exact results of the bond percolation model on the Bethe and the square-cactus lattice, respectively, in the presence of ghost field without recourse to the s →1 limit of the s -state Potts model.The critical exponents of the bond percolation model are calculated in the D (=2, 3,···)-dimensional simple cubic lattice on the basis of Suzuki's coherent anomaly method (CAM) by making use of a series of the pair, the square-cactus and the square approximations of the cluster variation method (CVM) in the s -state Potts model. These simple approximations give reasonable values of critical exponents α, β, γ and ν in comparison with ones estimated by other methods. It is also shown that the results of the pair and the square-cactus approximations can be derived as exact results of the bond percolation model on the Bethe and the square-cactus lattice, respectively, in the presence of ghost field without recourse to the s →1 limit of the s -state Potts model.

Journal of the Physical Society of JapanOct 15, 19915 citations

The critical exponents at the glass temperature

{T}_{g}

of a spin glass are estimated by making use of predictions obtained from a phase-space percolation model, in combination with scaling arguments. With this hypothesis, the whole set of exponents for a given system, including the dynamic exponent, can be expressed simply in terms of a single nonuniversal parameter. The model is checked against data from simulations and from three sets of experiments; agreement is very satisfactory.