26 research outputs found
Coarse grained models of stripe forming systems: phase diagrams, anomalies and scaling hypothesis
Two coarse-grained models which capture some universal characteristics of
stripe forming systems are stud- ied. At high temperatures, the structure
factors of both models attain their maxima on a circle in reciprocal space, as
a consequence of generic isotropic competing interactions. Although this is
known to lead to some universal properties, we show that the phase diagrams
have important differences, which are a consequence of the particular k
dependence of the fluctuation spectrum in each model. The phase diagrams are
computed in a mean field approximation and also after inclusion of small
fluctuations, which are shown to modify drastically the mean field behavior.
Observables like the modulation length and magnetization profiles are computed
for the whole temperature range accessible to both models and some important
differences in behavior are observed. A stripe compression modulus is computed,
showing an anomalous behavior with temperature as recently reported in related
models. Also, a recently proposed scaling hypothesis for modulated systems is
tested and found to be valid for both models studied.Comment: 9 pages, 13 figure
Event-Driven Monte Carlo: exact dynamics at all time-scales for discrete-variable models
We present an algorithm for the simulation of the exact real-time dynamics of
classical many-body systems with discrete energy levels. In the same spirit of
kinetic Monte Carlo methods, a stochastic solution of the master equation is
found, with no need to define any other phase-space construction. However,
unlike existing methods, the present algorithm does not assume any particular
statistical distribution to perform moves or to advance the time, and thus is a
unique tool for the numerical exploration of fast and ultra-fast dynamical
regimes. By decomposing the problem in a set of two-level subsystems, we find a
natural variable step size, that is well defined from the normalization
condition of the transition probabilities between the levels. We successfully
test the algorithm with known exact solutions for non-equilibrium dynamics and
equilibrium thermodynamical properties of Ising-spin models in one and two
dimensions, and compare to standard implementations of kinetic Monte Carlo
methods. The present algorithm is directly applicable to the study of the real
time dynamics of a large class of classical markovian chains, and particularly
to short-time situations where the exact evolution is relevant
Nature of Long-Range Order in Stripe-Forming Systems with Long-Range Repulsive Interactions
We study two dimensional stripe forming systems with competing repulsive
interactions decaying as . We derive an effective Hamiltonian with
a short range part and a generalized dipolar interaction which depends on the
exponent . An approximate map of this model to a known XY model with
dipolar interactions allows us to conclude that, for long range
orientational order of stripes can exist in two dimensions, and establish the
universality class of the models. When no long-range order is
possible, but a phase transition in the KT universality class is still present.
These two different critical scenarios should be observed in experimentally
relevant two dimensional systems like electronic liquids () and
dipolar magnetic films (). Results from Langevin simulations of
Coulomb and dipolar systems give support to the theoretical results.Comment: 5 pages, 2 figures. Supplemental Material include
The nematic phase in stripe forming systems within the self consistent screening approximation
We show that in order to describe the isotropic-nematic transition in stripe
forming systems with isotropic competing interactions of the Brazovskii class
it is necessary to consider the next to leading order in a 1/N approximation
for the effective Hamiltonian. This can be conveniently accomplished within the
self-consistent screening approximation. We solve the relevant equations and
show that the self-energy in this approximation is able to generate the
essential wave vector dependence to account for the anisotropic character of
two-point correlation function characteristic of a nematic phase.Comment: 8 pages, 4 figure