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

Damage Spreading in a Driven Lattice Gas Model

We studied damage spreading in a Driven Lattice Gas (DLG) model as a function of the temperature $T$, the magnitude of the external driving field $E$, and the lattice size. The DLG model undergoes an order-disorder second-order phase transition at the critical temperature $T_c(E)$, such that the ordered phase is characterized by high-density strips running along the direction of the applied field; while in the disordered phase one has a lattice-gas-like behaviour. It is found that the damage always spreads for all the investigated temperatures and reaches a saturation value $D_{sat}$ that depends only on $T$. $D_{sat}$ increases for $TT_c(E=\infty)$ and is free of finite-size effects. This behaviour can be explained as due to the existence of interfaces between the high-density strips and the lattice-gas-like phase whose roughness depends on $T$. Also, we investigated damage spreading for a range of finite fields as a function of $T$, finding a behaviour similar to that of the case with $E=\infty$.Comment: 13 pages, 7 figures. Submitted to "Journal of Statistical Mechanics: Theory and Experiment

Self-propelled Vicsek particles at low speed and low density

We study through numerical simulation the Vicsek model for very low speeds and densities. We consider scalar noise in two and three dimensions and vector noise in three dimensions. We focus on the behavior of the critical noise with density and speed, trying to clarify seemingly contradictory earlier results. We find that, for scalar noise, the critical noise is a power law in both density and speed, but although we confirm the density exponent in two dimensions, we find a speed exponent different from earlier reports (we consider lower speeds than previous studies). On the other hand, for the vector noise case we find that the dependence of the critical noise cannot be separated as a product of power laws in speed and density. Finally, we study the dependence of the relaxation time with speed. At the critical point we find a power law, with the same exponent in two and three dimensions.Fil: Rubio Puzzo, Maria Leticia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: De Virgiliis, Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina. Universidad Nacional de La Plata. Facultad de Ingeniería; ArgentinaFil: Grigera, Tomas Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentin

Damage spreading in a driven lattice gas model

We studied damage spreading in a Driven Lattice Gas (DLG) model as a function of the temperature T , the magnitude of the external driving field E, and the lattice size. The DLG model undergoes an order-disorder second-order phase transition at the critical temperature Tc (E), such that the ordered phase is characterized by high-density strips running along the direction of the applied field; while in the disordered phase one has a lattice-gas-like behavior. It is found that the damage always spreads for all the investigated temperatures and reaches a saturation value Dsat that depends only on T . Dsat increases for T Tc (E = ∞) and is free of finite-size effects. This behavior can be explained as due to the existence of interfaces between the high-density strips and the lattice-gas-like phase whose roughness depends on T . Also, we investigated damage spreading for a range of finite fields as a function of T , finding a behavior similar to that of the case with E = ∞.Instituto de Investigaciones Fisicoquímicas Teóricas y AplicadasInstituto de Física de Líquidos y Sistemas Biológico

Damage spreading in a driven lattice gas model

We studied damage spreading in a Driven Lattice Gas (DLG) model as a function of the temperature T , the magnitude of the external driving field E, and the lattice size. The DLG model undergoes an order-disorder second-order phase transition at the critical temperature Tc (E), such that the ordered phase is characterized by high-density strips running along the direction of the applied field; while in the disordered phase one has a lattice-gas-like behavior. It is found that the damage always spreads for all the investigated temperatures and reaches a saturation value Dsat that depends only on T . Dsat increases for T Tc (E = ∞) and is free of finite-size effects. This behavior can be explained as due to the existence of interfaces between the high-density strips and the lattice-gas-like phase whose roughness depends on T . Also, we investigated damage spreading for a range of finite fields as a function of T , finding a behavior similar to that of the case with E = ∞.Instituto de Investigaciones Fisicoquímicas Teóricas y AplicadasInstituto de Física de Líquidos y Sistemas Biológico

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.

Order-disorder criticality, wetting, and morphological phase transitions in the irreversible growth of far-from-equilibrium magnetic films

An exhaustive numerical investigation of the growth of magnetic films in confined $(d+1)$-dimensional stripped geometries ($d=1,2$) is carried out by means of extensive Monte Carlo simulations. Thin films in contact with a thermal bath are grown by adding spins with two possible orientations and considering ferromagnetic (nearest-neighbor) interactions. At low temperatures, it is observed that the films exhibit ``spontaneous magnetization reversals'' during the growth process. Furthermore, it is found that for $d=1$ the system is non-critical, while a continuous order-disorder phase transition at finite temperature takes place in the $d=2$ case. Using standard finite-size scaling procedures, the critical temperature and some relevant critical exponents are determined. Finally, the growth of magnetic films in $(2+1)$ dimensions with competing short-range magnetic fields acting along the confinement walls is studied. Due to the antisymmetric condition considered, an interface between domains with spins having opposite orientation develops along the growing direction. Such an interface undergoes a localization-delocalization transition that is the precursor of a wetting transition in the thermodynamic limit. Furthermore, the growing interface also undergoes morphological transitions in the growth mode. A comparison between the well-studied equilibrium Ising model and the studied irreversible magnetic growth model is performed throughout. Although valuable analogies are encountered, it is found that the nonequilibrium nature of the latter introduces new and rich physical features of interest.Comment: 23 pages, 10 figure