The fracton dynamics of percolating Heisenberg antiferromagnets are studied in terms of a dynamic scaling argument and large-scale numerical analysis. It is shown that the spectral (or fracton) dimension for antiferromagnetic fractons, $\tilde{d}_{\rm AF}$ , is bounded by the relation $\tilde{d}_{\rm AF}\le 1$ . The densities of states (DOS) are calculated for very large percolating antiferromagnets at the critical concentration p c formed on d =2, 3, and 4 simple cubic lattices. It is concluded, from the calculated DOS's, that the spectral dimensions $\tilde{d}_{\rm AF}$ are very close to unity for any Euclidean dimension d (≥2). We have also calculated the DOS for percolating antiferromagnets above p c in order to clarify the crossover behavior from extended magnons to fractons. In addition, the dynamical structure factor S ( q ,ω) is investigated both analytically and numerically. It is found, postulating a single-length scaling, that the asymptotic behaviors can be characterized by two exponents, the dynamical exponent z AF and a new exponent y . The numerical results for S ( q ,ω) support the validity of the single-length-scale postulate.The fracton dynamics of percolating Heisenberg antiferromagnets are studied in terms of a dynamic scaling argument and large-scale numerical analysis. It is shown that the spectral (or fracton) dimension for antiferromagnetic fractons, $\tilde{d}_{\rm AF}$, is bounded by the relation $\tilde{d}_{\rm AF}\le 1$. The densities of states (DOS) are calculated for very large percolating antiferromagnets at the critical concentration p c formed on d =2, 3, and 4 simple cubic lattices. It is concluded, from the calculated DOS's, that the spectral dimensions $\tilde{d}_{\rm AF}$ are very close to unity for any Euclidean dimension d (≥2). We have also calculated the DOS for percolating antiferromagnets above p c in order to clarify the crossover behavior from extended magnons to fractons. In addition, the dynamical structure factor S ( q ,ω) is investigated both analytically and numerically. It is found, postulating a single-length scaling, that the asymptotic behaviors can be characterized by two exponents, the dynamical exponent z AF and a new exponent y . The numerical results for S ( q ,ω) support the validity of the single-length-scale postulate.

Journal of the Physical Society of JapanSep 15, 199411 citations

Measures of critical exponents in the four-dimensional site percolation

H.G. Ballesteros, L.A. Fernández, V. Martín-Mayor +3 more

arXiv:hep-lat/9612024Physics Letters BMay 1, 199766 citations

Precise determination of the conductivity exponent of 3D percolation using exact numerical renormalization

J. P. Clerc, Viktor A. Podolskiy, Andrey Karlovich Sarychev

The European Physical Journal BMay 1, 200056 citations

Scaling properties of the dynamical structure factor of percolating Heisenberg antiferromagnets

Takamichi Terao, Kousuke Yakubo, Tsuneyoshi Nakayama

The scaling behavior of the dynamical structure factor S(q,\ensuremath{\omega}) of percolating Heisenberg antiferromagnets is investigated in terms of a dynamic scaling argument and numerical calculations. It is found, based on the single-length-scaling postulate, that the asymptotic behavior of S(q,\ensuremath{\omega}) can be characterized by only two exponents: the dynamic exponent ${\mathit{z}}_{\mathit{a}}$ and a new exponent y. This theoretical prediction is confirmed by direct numerical calculations. The values of the exponents ${\mathit{z}}_{\mathit{a}}$ and y are determined for the case of d=2 percolating Heisenberg antiferromagnets.The scaling behavior of the dynamical structure factor S(q,\ensuremath{\omega}) of percolating Heisenberg antiferromagnets is investigated in terms of a dynamic scaling argument and numerical calculations. It is found, based on the single-length-scaling postulate, that the asymptotic behavior of S(q,\ensuremath{\omega}) can be characterized by only two exponents: the dynamic exponent ${\mathit{z}}_{\mathit{a}}$ and a new exponent y. This theoretical prediction is confirmed by direct numerical calculations. The values of the exponents ${\mathit{z}}_{\mathit{a}}$ and y are determined for the case of d=2 percolating Heisenberg antiferromagnets.

Physical review. B, Condensed matterMay 1, 19947 citations

Critical dynamics in Heisenberg ferromagnets and antiferromagnets near the percolation threshold

Iveta R. Pimentel, Robin B. Stinchcombe

The critical spin-wave dynamics of dilute ferromagnetic and antiferromagnetic Heisenberg systems near the percolation threshold is studied on a two-dimensional regular (fractal) model for bond percolation, which captures the relevant geometric features of the cluster structure. The dynamic critical exponent and spectral dimension for both the ferromagnetic and antiferromagnetic systems are calculated. The treatment of the dynamics in these systems requires the use of generalised scaling techniques for sublattice systems, which involve an extension of the parameter space.The critical spin-wave dynamics of dilute ferromagnetic and antiferromagnetic Heisenberg systems near the percolation threshold is studied on a two-dimensional regular (fractal) model for bond percolation, which captures the relevant geometric features of the cluster structure. The dynamic critical exponent and spectral dimension for both the ferromagnetic and antiferromagnetic systems are calculated. The treatment of the dynamics in these systems requires the use of generalised scaling techniques for sublattice systems, which involve an extension of the parameter space.

Journal of Physics A Mathematical and GeneralSep 21, 19894 citations

Universality test for critical amplitudes in two dimensional percolation

Joaquín Marro

Physics Letters ANov 1, 197612 citations

\tilde{d}_{\rm AF}

, is bounded by the relation

\tilde{d}_{\rm AF}\le 1

. The densities of states (DOS) are calculated for very large percolating antiferromagnets at the critical concentration p c formed on d =2, 3, and 4 simple cubic lattices. It is concluded, from the calculated DOS's, that the spectral dimensions

\tilde{d}_{\rm AF}

are very close to unity for any Euclidean dimension d (≥2). We have also calculated the DOS for percolating antiferromagnets above p c in order to clarify the crossover behavior from extended magnons to fractons. In addition, the dynamical structure factor S ( q ,ω) is investigated both analytically and numerically. It is found, postulating a single-length scaling, that the asymptotic behaviors can be characterized by two exponents, the dynamical exponent z AF and a new exponent y . The numerical results for S ( q ,ω) support the validity of the single-length-scale postulate.

{\mathit{z}}_{\mathit{a}}

and a new exponent y. This theoretical prediction is confirmed by direct numerical calculations. The values of the exponents

{\mathit{z}}_{\mathit{a}}

and y are determined for the case of d=2 percolating Heisenberg antiferromagnets.