Short-Time Critical Dynamics of Damage Spreading in the Two-Dimensional Ising Model

The short-time critical dynamics of propagation of damage in the Ising ferromagnet in two dimensions is studied by means of Monte Carlo simulations. Starting with equilibrium configurations at $T= \infty$ and magnetization $M=0$, an initial damage is created by flipping a small amount of spins in one of the two replicas studied. In this way, the initial damage is proportional to the initial magnetization $M_0$ in one of the configurations upon quenching the system at $T_C$, the Onsager critical temperature of the ferromagnetic-paramagnetic transition. It is found that, at short times, the damage increases with an exponent $\theta_D=1.915(3)$, which is much larger than the exponent $\theta=0.197$ characteristic of the initial increase of the magnetization $M(t)$. Also, an epidemic study was performed. It is found that the average distance from the origin of the epidemic ($\langle R^2(t)\rangle$) grows with an exponent $z^* \approx \eta \approx 1.9$, which is the same, within error bars, as the exponent $\theta_D$. However, the survival probability of the epidemics reaches a plateau so that $\delta=0$. On the other hand, by quenching the system to lower temperatures one observes the critical spreading of the damage at $T_{D}\simeq 0.51 T_C$, where all the measured observables exhibit power laws with exponents $\theta_D = 1.026(3)$, $\delta = 0.133(1)$, and $z^*=1.74(3)$.Comment: 11 pages, 9 figures (included). Phys. Rev. E (2010), in press

Ground-state configuration space heterogeneity of random finite-connectivity spin glasses and random constraint satisfaction problems

We demonstrate through two case studies, one on the p-spin interaction model and the other on the random K-satisfiability problem, that a heterogeneity transition occurs to the ground-state configuration space of a random finite-connectivity spin glass system at certain critical value of the constraint density. At the transition point, exponentially many configuration communities emerge from the ground-state configuration space, making the entropy density s(q) of configuration-pairs a non-concave function of configuration-pair overlap q. Each configuration community is a collection of relatively similar configurations and it forms a stable thermodynamic phase in the presence of a suitable external field. We calculate s(q) by the replica-symmetric and the first-step replica-symmetry-broken cavity methods, and show by simulations that the configuration space heterogeneity leads to dynamical heterogeneity of particle diffusion processes because of the entropic trapping effect of configuration communities. This work clarifies the fine structure of the ground-state configuration space of random spin glass models, it also sheds light on the glassy behavior of hard-sphere colloidal systems at relatively high particle volume fraction.Comment: 26 pages, 9 figures, submitted to Journal of Statistical Mechanic

Scaling of spin avalanches in growing networks

Growing networks decorated with antiferromagnetically coupled spins are archetypal examples of complex systems due to the frustration and the multivalley character of their energy landscapes. Here we use the damage spreading method (DS) to investigate the cohesion of spin avalanches in the exponential networks and the scale-free networks. On the contrary to the conventional methods, the results obtained from DS suggest that the avalanche spectra are characterized by the same statistics as the degree distribution in their home networks. Further, the obtained mean range $Z$ of an avalanche, i.e. the maximal distance reached by an avalanche from the damaged site, scales with the avalanche size $s$ as $Z/N^\beta =f(s/N^{\alpha})$, where $\alpha=0.5$ and $\beta=0.33$. These values are true for both kinds of networks for the number $M$ of nodes to which new nodes are attached between 4 and 10; a check for M=25 confirms these values as well.Comment: 10 pages, 9 figures. More data in Fig.

Study of Damage Propagation at the Interface Localization-Delocalization Transition of the Confined Ising Model

The propagation of damage in a confined magnetic Ising film, with short range competing magnetic fields ($h$) acting at opposite walls, is studied by means of Monte Carlo simulations. Due to the presence of the fields, the film undergoes a wetting transition at a well defined critical temperature $T_w(h)$. In fact, the competing fields causes the occurrence of an interface between magnetic domains of different orientation. For $T T_w(h)$) such interface is bounded (unbounded) to the walls, while right at $T_w(h)$ the interface is essentially located at the center of the film. It is found that the spatio-temporal spreading of the damage becomes considerably enhanced by the presence of the interface, which act as a ''catalyst'' of the damage causing an enhancement of the total damaged area. The critical points for damage spreading are evaluated by extrapolation to the thermodynamic limit using a finite-size scaling approach. Furthermore, the wetting transition effectively shifts the location of the damage spreading critical points, as compared with the well known critical temperature of the order-disorder transition characteristic of the Ising model. Such a critical points are found to be placed within the non-wet phase.Comment: 22 pages, 13 figures include

Damage spreading and ferromagnetic order in the three-dimensional ±J Edwards-Anderson spin glass model

Using information of the ground-state topology we show that the damage spreading technique unveils ferromagnetic order in the three-dimensional ±J Edwards-Anderson spin glass model. With spin-flipping dynamics damage spreads for temperatures larger than Tg, the glass transition temperature. With spin-orienting dynamics and for temperatures in Tg<T<Td, damage spreads over a finite region of the system, composed of finite clusters of ferromagnetic character. Td is the spin-orienting damage critical temperature, which is of the same order as the critical temperature of the ferromagnetic Ising model, Tc. The present results allow for an interpretation within a single framework of known —and sometimes puzzling— results, giving an intuitive picture for growing order in spin glasses

Hyperfine Characterization of Pure and Doped Zircons

The aim of this work has been to investigate the influence of two coloring dopant ions on the ZrSio4 host lattice, Pure, vanadium-doped and praseodymium-doped zircon powders have been synthesized by the ceramic method and analyzed using X-ray diffraction and perturbed angular correlations (PAC) hyperfine technique which probes the nearest environments of zirconium ions

Hyperfine Characterization of Pure and Doped Zircons

The aim of this work has been to investigate the influence of two coloring dopant ions on the ZrSio4 host lattice, Pure, vanadium-doped and praseodymium-doped zircon powders have been synthesized by the ceramic method and analyzed using X-ray diffraction and perturbed angular correlations (PAC) hyperfine technique which probes the nearest environments of zirconium ions