We investigate a $(d+1)$ -dimensional ``correlated'' random-field system with d spatial dimensions and one Trotter dimension along which randomness is ``correlated'' or striped. In the sense of universality this model is equivalent to a d-dimensional quantum random-field system. We investigate the dissipative Langevin dynamics of this ``striped'' $(d+1)$ -dimensional systems within a replica symmetric framework, employing the perturbative $\ensuremath{\epsilon}$ expansion around the upper critical dimension to explore the effect of an additional dimension (along which the randomness is correlated) on the dynamical scaling. We argue that the $\ensuremath{\epsilon}$ expansion fails to capture the activated nature of dynamics. We also extend the phenomenological renormalization-group calculations to investigate the critical behavior of a $(d+1)$ -dimensional correlated random-field Ising systems.We investigate a $(d+1)$-dimensional ``correlated'' random-field system with d spatial dimensions and one Trotter dimension along which randomness is ``correlated'' or striped. In the sense of universality this model is equivalent to a d-dimensional quantum random-field system. We investigate the dissipative Langevin dynamics of this ``striped'' $(d+1)$-dimensional systems within a replica symmetric framework, employing the perturbative $\ensuremath{\epsilon}$ expansion around the upper critical dimension to explore the effect of an additional dimension (along which the randomness is correlated) on the dynamical scaling. We argue that the $\ensuremath{\epsilon}$ expansion fails to capture the activated nature of dynamics. We also extend the phenomenological renormalization-group calculations to investigate the critical behavior of a $(d+1)$-dimensional correlated random-field Ising systems.

Physical review. B, Condensed matterJan 1, 20003 citations

One-Dimensional Random Systems with Long Range Interactions.

B. Gabriel Kotliar

Jan 1, 19830 citations

Coupling of Random Systems

David Lanzenberger, Ueli M. Maurer

Lecture notes in computer scienceJan 1, 20207 citations

The dynamics of one-dimensional random quantumXYsystem with Dzyaloshinskii—Moriya interaction

Yin-Fang Li, Xiang-Mu Kong

In this paper, the effects of random variables on the dynamics of the s = 1/2 XY model with the Dzyaloshinskii-Moriya interaction are studied. By means of the recurrence relation method in the high-temperature limit, we calculate the spin autocorrelation functions as well as the corresponding spectral densities for the cases that the exchange couplings between spins or external magnetic fields satisfy the double-Gaussian distribution. It is found that when the standard deviation of random exchange coupling δ J (or the standard deviation of random external field δ B ) is small, the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one. However, when δ J (or δ B ) is large, the crossover vanishes, and the system shows a central-peak behavior or the most disordered one. We also analyze the cases in which the exchange couplings or the external fields satisfy the bimodal and the Gaussian distributions. Our results show that for all the cases considered, the dynamics of the above system is similar to that of the one-dimensional random XY model.In this paper, the effects of random variables on the dynamics of the s = 1/2 XY model with the Dzyaloshinskii-Moriya interaction are studied. By means of the recurrence relation method in the high-temperature limit, we calculate the spin autocorrelation functions as well as the corresponding spectral densities for the cases that the exchange couplings between spins or external magnetic fields satisfy the double-Gaussian distribution. It is found that when the standard deviation of random exchange coupling δ J (or the standard deviation of random external field δ B ) is small, the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one. However, when δ J (or δ B ) is large, the crossover vanishes, and the system shows a central-peak behavior or the most disordered one. We also analyze the cases in which the exchange couplings or the external fields satisfy the bimodal and the Gaussian distributions. Our results show that for all the cases considered, the dynamics of the above system is similar to that of the one-dimensional random XY model.

Chinese Physics BMar 1, 201310 citations

Effects of random external fields on the dynamics of the one-dimensional Blume-Capel model

Li Yin-Fang, Shen Yin-Yang, Xiang-Mu Kong

The dynamical properties of quantum spin systems have received a great deal of theoretical and experimental attention in the past decades. Only recently, has much attention been paid to the random quantum spin systems. In this paper the effect of random external field on the dynamics of one-dimensional Blume-Capel model with s = 1 in the high-temperature limit is investigated by using the recurrence relations method. The spin autocorrelation function as well as the corresponding spectral density of the system is calculated in the presence of the field that satisfies two types of distributions. When the single-ion anisotropy takes 0, for the bimodal distribution, the dynamics of the system behaves as a crossover from a central peak behavior to a collective mode one. For the Gaussian distribution, when the standard deviation is small, the dynamical behavior of the system also exhibits a crossover; when the standard deviation is large enough, the system only shows a disordered behavior. We also discuss the effect of the single-ion anisotropy on the dynamical property of the system, and find that the collective-mode behavior becomes weaker as the single-ion anisotropy exists.The dynamical properties of quantum spin systems have received a great deal of theoretical and experimental attention in the past decades. Only recently, has much attention been paid to the random quantum spin systems. In this paper the effect of random external field on the dynamics of one-dimensional Blume-Capel model with s = 1 in the high-temperature limit is investigated by using the recurrence relations method. The spin autocorrelation function as well as the corresponding spectral density of the system is calculated in the presence of the field that satisfies two types of distributions. When the single-ion anisotropy takes 0, for the bimodal distribution, the dynamics of the system behaves as a crossover from a central peak behavior to a collective mode one. For the Gaussian distribution, when the standard deviation is small, the dynamical behavior of the system also exhibits a crossover; when the standard deviation is large enough, the system only shows a disordered behavior. We also discuss the effect of the single-ion anisotropy on the dynamical property of the system, and find that the collective-mode behavior becomes weaker as the single-ion anisotropy exists.

Acta Physica SinicaJan 1, 20125 citations

Instability in one-dimensional systems

Bikiran Prasad Barua, S.K. Sinha

Physics Letters AOct 1, 19790 citations

We investigate a

(d+1)

-dimensional ``correlated'' random-field system with d spatial dimensions and one Trotter dimension along which randomness is ``correlated'' or striped. In the sense of universality this model is equivalent to a d-dimensional quantum random-field system. We investigate the dissipative Langevin dynamics of this ``striped''

(d+1)

-dimensional systems within a replica symmetric framework, employing the perturbative $\ensuremath{\epsilon}$ expansion around the upper critical dimension to explore the effect of an additional dimension (along which the randomness is correlated) on the dynamical scaling. We argue that the $\ensuremath{\epsilon}$ expansion fails to capture the activated nature of dynamics. We also extend the phenomenological renormalization-group calculations to investigate the critical behavior of a

(d+1)

-dimensional correlated random-field Ising systems.