The computer simulations of the critical dynamics of the structurally disordered three-dimensional Ising model are performed by the damage spreading method. For the systems with spin densities p = 0.6 and 0.8, we calculate the critical temperature and dynamic critical exponent z characterizing the behavior of relaxation properties near the critical point. The analysis of the results demonstrates the nonuniversality of the critical dynamics in the disordered Ising model. To interpret such dynamics, we introduce the concept of two universal types of critical behavior corresponding to weak and strong disorder, respectively.The computer simulations of the critical dynamics of the structurally disordered three-dimensional Ising model are performed by the damage spreading method. For the systems with spin densities p = 0.6 and 0.8, we calculate the critical temperature and dynamic critical exponent z characterizing the behavior of relaxation properties near the critical point. The analysis of the results demonstrates the nonuniversality of the critical dynamics in the disordered Ising model. To interpret such dynamics, we introduce the concept of two universal types of critical behavior corresponding to weak and strong disorder, respectively.

Journal of Experimental and Theoretical Physics LettersJan 1, 20155 citations

Dynamic scaling of disordered Ising systems

Hans-O Heuer

The critical dynamics of site-disordered three-dimensional Ising systems has been studied by conventional local dynamics simulations investing 10 15 single spin flips. The author has verified that the correlation functions of disordered Ising systems obey dynamic scaling behaviour. The dynamic scaling functions have been calculated. The critical exponent z appears to be strongly dependent on the degree of disorder. The author has shown that this dependence arises from a crossover phenomenon which has been detected in the static critical behaviour. The dynamical exponent has been estimated to be z=2.4+or-0.1 which is surprisingly near to the renormalization group result in O( in 1/2).The critical dynamics of site-disordered three-dimensional Ising systems has been studied by conventional local dynamics simulations investing 10 15 single spin flips. The author has verified that the correlation functions of disordered Ising systems obey dynamic scaling behaviour. The dynamic scaling functions have been calculated. The critical exponent z appears to be strongly dependent on the degree of disorder. The author has shown that this dependence arises from a crossover phenomenon which has been detected in the static critical behaviour. The dynamical exponent has been estimated to be z=2.4+or-0.1 which is surprisingly near to the renormalization group result in O( in 1/2).

Journal of Physics A Mathematical and GeneralMar 21, 199337 citations

On the critical dynamics of spin-glasses

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

Physics Letters AMar 1, 19771 citation

Dynamic critical behavior of random spin chains in a field

Iveta R. Pimentel, Robin B. Stinchcombe

The dynamic critical behavior of one-dimensional random spin systems in a field at zero temperature is investigated by a generalized transfer-matrix scaling technique. Three spin models are considered: Heisenberg in a longitudinal field, XY in a transverse field, and Ising in a transverse field, with either spin-glass or random-field disorder. Near the transition, i.e., for small values of the reduced field \ensuremath{\Delta}=(H- ${H}_{c}$ ), where ${H}_{c}$ is the critical field, one finds that the dispersion relation for the low-frequency \ensuremath{\omega}, small-wave-vector k spin-wave excitations takes the scaling form \ensuremath{\omega}= ${k}^{z}$ f(\ensuremath{\Delta}/ ${k}^{\mathrm{cphi}}$ ), and exact results are given for the dynamic exponent z and crossover exponent cphi. This form contains a crossover of the frequency \ensuremath{\omega} between two different asymptotic behaviors: ${k}^{z}$ for \ensuremath{\Delta}\ensuremath{\ll} ${k}^{\mathrm{cphi}}$ and ${h}^{\ensuremath{\delta}}$ for \ensuremath{\Delta}\ensuremath{\gg} ${k}^{\mathrm{cphi}}$ , where the field exponent is \ensuremath{\delta}=z/cphi. In the case of the Heisenberg systems the spin-glass disorder gives rise to the nontrivial dynamic exponent z=(3/2, whereas in the random-field case it is the exponent associated to the field that becomes nontrivial, taking the value (4/3. For the transverse XY systems the random-field disorder implies nontrivial values for both the dynamic and field exponents, (3/2 and (3/4, respectively, whereas the spin-glass disorder does not affect the dynamics of the system, which behaves like a pure transverse XY ferromagnet. Finally, for the transverse Ising systems neither the random field nor the spin-glass disorder affects the dynamics, which is the same as for a pure transverse Ising ferromagnet.The dynamic critical behavior of one-dimensional random spin systems in a field at zero temperature is investigated by a generalized transfer-matrix scaling technique. Three spin models are considered: Heisenberg in a longitudinal field, XY in a transverse field, and Ising in a transverse field, with either spin-glass or random-field disorder. Near the transition, i.e., for small values of the reduced field \ensuremath{\Delta}=(H-${H}_{c}$), where ${H}_{c}$ is the critical field, one finds that the dispersion relation for the low-frequency \ensuremath{\omega}, small-wave-vector k spin-wave excitations takes the scaling form \ensuremath{\omega}=${k}^{z}$f(\ensuremath{\Delta}/${k}^{\mathrm{cphi}}$), and exact results are given for the dynamic exponent z and crossover exponent cphi. This form contains a crossover of the frequency \ensuremath{\omega} between two different asymptotic behaviors: ${k}^{z}$ for \ensuremath{\Delta}\ensuremath{\ll}${k}^{\mathrm{cphi}}$ and ${h}^{\ensuremath{\delta}}$ for \ensuremath{\Delta}\ensuremath{\gg}${k}^{\mathrm{cphi}}$, where the field exponent is \ensuremath{\delta}=z/cphi. In the case of the Heisenberg systems the spin-glass disorder gives rise to the nontrivial dynamic exponent z=(3/2, whereas in the random-field case it is the exponent associated to the field that becomes nontrivial, taking the value (4/3. For the transverse XY systems the random-field disorder implies nontrivial values for both the dynamic and field exponents, (3/2 and (3/4, respectively, whereas the spin-glass disorder does not affect the dynamics of the system, which behaves like a pure transverse XY ferromagnet. Finally, for the transverse Ising systems neither the random field nor the spin-glass disorder affects the dynamics, which is the same as for a pure transverse Ising ferromagnet.

Physical review. B, Condensed matterSep 1, 19899 citations

{H}_{c}

), where

{H}_{c}

is the critical field, one finds that the dispersion relation for the low-frequency \ensuremath{\omega}, small-wave-vector k spin-wave excitations takes the scaling form \ensuremath{\omega}=

{k}^{z}

f(\ensuremath{\Delta}/

{k}^{\mathrm{cphi}}

), and exact results are given for the dynamic exponent z and crossover exponent cphi. This form contains a crossover of the frequency \ensuremath{\omega} between two different asymptotic behaviors:

{k}^{z}

for \ensuremath{\Delta}\ensuremath{\ll}

{k}^{\mathrm{cphi}}

and ${h}^{\ensuremath{\delta}}$ for \ensuremath{\Delta}\ensuremath{\gg}

{k}^{\mathrm{cphi}}

, where the field exponent is \ensuremath{\delta}=z/cphi. In the case of the Heisenberg systems the spin-glass disorder gives rise to the nontrivial dynamic exponent z=(3/2, whereas in the random-field case it is the exponent associated to the field that becomes nontrivial, taking the value (4/3. For the transverse XY systems the random-field disorder implies nontrivial values for both the dynamic and field exponents, (3/2 and (3/4, respectively, whereas the spin-glass disorder does not affect the dynamics of the system, which behaves like a pure transverse XY ferromagnet. Finally, for the transverse Ising systems neither the random field nor the spin-glass disorder affects the dynamics, which is the same as for a pure transverse Ising ferromagnet.