7 research outputs found
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 and magnetization
, 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 in one of the configurations upon quenching the
system at , the Onsager critical temperature of the
ferromagnetic-paramagnetic transition. It is found that, at short times, the
damage increases with an exponent , which is much larger
than the exponent characteristic of the initial increase of the
magnetization . Also, an epidemic study was performed. It is found that
the average distance from the origin of the epidemic ()
grows with an exponent , which is the same,
within error bars, as the exponent . However, the survival
probability of the epidemics reaches a plateau so that . On the other
hand, by quenching the system to lower temperatures one observes the critical
spreading of the damage at , where all the measured
observables exhibit power laws with exponents , , and .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 , the magnitude of the external driving field , and
the lattice size. The DLG model undergoes an order-disorder second-order phase
transition at the critical temperature , 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 that depends only on .
increases for 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 . Also, we investigated damage spreading for a range of
finite fields as a function of , finding a behaviour similar to that of the
case with .Comment: 13 pages, 7 figures. Submitted to "Journal of Statistical Mechanics:
Theory and Experiment
Damage Spreading at the Corner Filling Transition in the two-dimensional Ising Model
The propagation of damage on the square Ising lattice with a corner geometry
is studied by means of Monte Carlo simulations. It is found that, just at
(critical temperature of the filling transition) the damage
initially propagates along the interface of the competing domains, according to
a power law given by . The value obtained for the
dynamic exponent () is in agreement with that corresponding
to the wetting transition in the slit geometry (Abraham Model) given by
. However, for later times the propagation crosses to a
new regime such as , which is due to the propagation
of the damage into the bulk of the magnetic domains. This result can be
understood due to the constraints imposed to the propagation of damage by the
corner geometry of the system that cause healing at the corners where the
interface is attached.Comment: 22 pages, including figures Submited to J. Phys.: Condens. Matte
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 () 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 .
In fact, the competing fields causes the occurrence of an interface between
magnetic domains of different orientation. For ) such
interface is bounded (unbounded) to the walls, while right at 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