55 research outputs found
A new comprehensive study of the 3D random-field Ising model via sampling the density of states in dominant energy subspaces
The three-dimensional bimodal random-field Ising model is studied via a new
finite temperature numerical approach. The methods of Wang-Landau sampling and
broad histogram are implemented in a unified algorithm by using the N-fold
version of the Wang-Landau algorithm. The simulations are performed in dominant
energy subspaces, determined by the recently developed critical minimum energy
subspace technique. The random fields are obtained from a bimodal distribution,
that is we consider the discrete case and the model is studied on
cubic lattices with sizes . In order to extract information
for the relevant probability distributions of the specific heat and
susceptibility peaks, large samples of random field realizations are generated.
The general aspects of the model's scaling behavior are discussed and the
process of averaging finite-size anomalies in random systems is re-examined
under the prism of the lack of self-averaging of the specific heat and
susceptibility of the model.Comment: 10 pages, 4 figures, presented at the third NEXT Sigma Phi
International Conference, Kolymbari, Greece (2005
A study for the static properties of symmetric linear multiblock copolymers under poor solvent conditions
We use a standard bead-spring model and molecular dynamics simulations to
study the static properties of symmetric linear multiblock copolymer chains and
their blocks under poor solvent conditions in a dilute solution from the regime
close to theta conditions, where the chains adopt a coil-like formation, to the
poorer solvent regime where the chains collapse obtaining a globular formation
and phase separation between the blocks occurs. We choose interaction
parameters as is done for a standard model, i.e., the Lennard-Jones fluid and
we consider symmetric chains, i.e., the multiblock copolymer consists of an
even number of alternating chemically different A and B blocks of the same
length . We show how usual static properties of the individual
blocks and the whole multiblock chain can reflect the phase behavior of such
macromolecules. Also, how parameters, such as the number of blocks can
affect properties of the individual blocks, when chains are in a poor solvent
for a certain range of . A detailed discussion of the static properties of
these symmetric multiblock copolymers is also given. Our results in combination
with recent simulation results on the behavior of multiblock copolymer chains
provide a complete picture for the behavior of these macromolecules under poor
solvent conditions, at least for this most symmetrical case. Due to the
standard choice of our parameters, our system can be used as a benchmark for
related models, which aim at capturing the basic aspects of the behavior of
various biological systems.Comment: 13 pages, 11 figure
Geometry effects in the magnetoconductance of normal and Andreev Sinai billiards
We study the transport properties of low-energy (quasi)particles
ballistically traversing normal and Andreev two-dimensional open cavities with
a Sinai-billiard shape. We consider four different geometrical setups and focus
on the dependence of transport on the strength of an applied magnetic field. By
solving the classical equations of motion for each setup we calculate the
magnetoconductance in terms of transmission and reflection coefficients for
both the normal and Andreev versions of the billiard, calculating in the latter
the critical field value above which the outgoing current of holes becomes
zero.Comment: 4 pages, 4 figure
Self-assembly of DNA-functionalized colloids
Colloidal particles grafted with single-stranded DNA (ssDNA) chains can self-assemble into a number of different crystalline structures, where hybridization of the ssDNA chains creates links between colloids stabilizing their structure. Depending on the geometry and the size of the particles, the grafting density of the ssDNA chains, and the length and choice of DNA sequences, a number of different crystalline structures can be fabricated. However, understanding how these factors contribute synergistically to the self-assembly process of DNA-functionalized nano- or micro-sized particles remains an intensive field of research. Moreover, the fabrication of long-range structures due to kinetic bottlenecks in the self-assembly are additional challenges. Here, we discuss the most recent advances from theory and experiment with particular focus put on recent simulation studies
Critical dynamical behavior of the Ising model
We investigate the dynamical critical behavior of the two- and
three-dimensional Ising model with Glauber dynamics. In contrast to the usual
standing, we focus on the mean-squared deviation of the magnetization ,
MSD, as a function of time, as well as on the autocorrelation function of
. These two functions are distinct but closely related. We find that MSD
features a first crossover at time , from ordinary
diffusion with MSD , to anomalous diffusion with MSD . Purely on numerical grounds, we obtain the values and
for the two-dimensional Ising ferromagnet. Related to this,
the magnetization autocorrelation function crosses over from an exponential
decay to a stretched-exponential decay. At later times, we find a second
crossover at time . Here, MSD saturates to its
late-time value , while the autocorrelation function
crosses over from stretched-exponential decay to simple exponential one. We
also confirm numerically the value , earlier reported as the
single dynamic exponent. Continuity of MSD requires that
. We speculate that and
, values that indeed lead to the expected result.
A complementary analysis for the three-dimensional Ising model provides the
estimates , , and . While
has attracted significant attention in the literature, we argue that
for all practical purposes is more important, as it determines the
number of statistically independent measurements during a long simulation.Comment: 6 pages, 6 figure
Geometric clusters in the overlap of the Ising model
We study the percolation properties of geometrical clusters defined in the overlap space of two statistically independent replicas of a square-lattice Ising model that are simulated at the same temperature. In particular, we consider two distinct types of clusters in the overlap, which we dub soft- and hard-constraint clusters, and which are subsets of the regions of constant spin overlap. By means of Monte Carlo simulations and a finite-size scaling analysis we estimate the transition temperature as well as the set of critical exponents characterizing the percolation transitions undergone by these two cluster types. The results suggest that both soft- and hard-constraint clusters percolate at the critical temperature of the Ising model and their critical behavior is governed by the correlation-length exponent ν=1 found by Onsager. At the same time, they exhibit nonstandard and distinct sets of exponents for the average cluster size and percolation strength
Thermodynamic properties of disordered quantum spin ladders
In this paper, we study the thermodynamic properties of spin- antiferromagnetic Heisenberg ladders by means of the stochastic series expansion quantum Monte Carlo technique. This includes the thermal properties of the specific heat, uniform and staggered susceptibilities, spin gap, and structure factor. Our numerical simulations are probed over a large ensemble of random realizations in a wide range of disorder strengths , from the clean () case up to the diluted () limit, and for selected choices of number of legs per site. Our results show some interesting phenomena, like the presence of crossing points in the temperature plane for both the specific heat and uniform susceptibility curves which appear to be universal in , as well as a variable dependence of the spin gap in the amount of disorder upon increasing
Finite-size scaling of the random-field Ising model above the upper critical dimension
Finite-size scaling above the upper critical dimension is a long-standing
puzzle in the field of Statistical Physics. Even for pure systems various
scaling theories have been suggested, partially corroborated by numerical
simulations. In the present manuscript we address this problem in the even more
complicated case of disordered systems. In particular, we investigate the
scaling behavior of the random-field Ising model at dimension , i.e.,
above its upper critical dimension , by employing extensive
ground-state numerical simulations. Our results confirm the hypothesis that at
dimensions , linear length scale should be replaced in
finite-size scaling expressions by the effective scale . Via a fitted version of the quotients method that takes this
modification, but also subleading scaling corrections into account, we compute
the critical point of the transition for Gaussian random fields and provide
estimates for the full set of critical exponents. Thus, our analysis indicates
that this modified version of finite-size scaling is successful also in the
context of the random-field problem.Comment: 19 pages preprint style, 5 figures, Appendix include
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