arXiv subjects

Nikolaos G. Fytas

Publications and source records attributed to Nikolaos G. Fytas.

52 records · Page 3Linked to original sources

arXiv2016

Phase transitions in disordered systems: the example of the random-field Ising model in four dimensions

By performing a high-statistics simulation of the $D=4$ random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high accuracy the complete set of critical exponents for this class, including the correction-to-scaling exponent. Our results indicate that in four dimensions: (i) dimensional reduction as predicted by the perturbative renormalization group does not hold and (ii) three independent critical exponents are needed to described the transition.

cond-mat.dis-nn↗

arXiv2016

Bridges in the random-cluster model

The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By introducing a classification of edges based on their relevance to the connectivity we study the stability of clusters in this model. We derive several exact relations for general graphs that allow us to derive unambiguously the finite-size scaling behavior of the density of bridges and non-bridges. For percolation, we are also able to characterize the point for which clusters become maximally fragile and show that it is connected to the concept of the bridge load. Combining our exact treatment with further results from conformal field theory, we uncover a surprising behavior of the variance of the number of (non-)bridges, showing that these diverge in two dimensions below the value $4\cos^2{(π/\sqrt{3})}=0.2315891\cdots$ of the cluster coupling $q$. Finally, it is shown that a partial or complete pruning of bridges from clusters enables estimates of the backbone fractal dimension that are much less encumbered by finite-size corrections than more conventional approaches.

cond-mat.stat-mech↗

arXiv2015

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.

cond-mat.soft↗

arXiv2015

Fragmentation of fractal random structures

We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model allows us to discuss a wide range of systems with fractal properties including trees as well as dense clusters. We present exact results for the densities of fragmenting edges and the distribution of fragment sizes for critical clusters in two dimensions. Dynamical fragmentation with a size cutoff leads to broad distributions of fragment sizes. The resulting power laws are shown to encode characteristic fingerprints of the fragmented objects.

cond-mat.stat-mech↗

arXiv2015

Parallel multicanonical study of the three-dimensional Blume-Capel model

We study the thermodynamic properties of the three-dimensional Blume-Capel model on the simple cubic lattice by means of computer simulations. In particular, we implement a parallelized variant of the multicanonical approach and perform simulations by keeping a constant temperature and crossing the phase boundary along the crystal-field axis. We obtain numerical data for several temperatures in both the first- and second-order regime of the model. Finite-size scaling analyses provide us with transition points and the dimensional scaling behavior in the numerically demanding first-order regime, as well as a clear verification of the expected Ising universality in the respective second-order regime. Finally, we discuss the scaling behavior in the vicinity of the tricritical point.

cond-mat.stat-mech↗

arXiv2014

Phase behaviour of two-component bottle-brush polymers with flexible backbones under poor solvent conditions

The phase behaviour of two-component bottle-brush polymers with fully flexible backbones under poor solvent conditions is studied via molecular-dynamics simulations, using a coarse-grained bead-spring model and side chains of up to $N=40$ effective monomers. We consider a symmetric model where side chains of type A and B are grafted alternately onto a flexible backbone. The aim of this study to explore the phase behaviour of two-component bottle-brushes depending on parameters, such as as the grafting density $σ$, the backbone length $N_b$, the side-chain length $N$, and the temperature $T$. Based on a cluster analysis, we identify for our range of parameters the regimes of fully phase separated systems, i.e., A-type side chains form one cluster and B-type chains another, while the interface that separates these two clusters contains the backbone monomers. We find that pearl-necklace or Janus-like structures, which normally occur for bottle-brush polymers with rigid backbones under poor solvent conditions, are fully attributed to the backbone rigidity, and, therefore, such structures are unlikely in the case of bottle brushes with fully flexible backbones. Also, a comparative discussion with earlier work on the phase behaviour of single-component bottle-brush polymers with flexible backbones is performed.

cond-mat.soft↗

arXiv2013

Molecular dynamics simulations of single-component bottle-brush polymers with a flexible backbone under poor solvent conditions

Conformations of a single-component bottle-brush polymer with a fully flexible backbone under poor solvent conditions are studied by molecular-dynamics simulations, using a coarse-grained bead-spring model with side chains of up to N=40 effective monomers. By variation of the solvent quality and the grafting density $σ$ with which side chains are grafted onto the flexible backbone, we study for backbone lengths of up to $N_b=100$ the crossover from the brush/coil regime to the dense collapsed state. At lower temperatures, where collapsed chains with a constant monomer density are observed, the choice of the above parameters does not play any role and it is the total number of monomers that defines the dimensions of the chains. Furthermore, bottle-brush polymers with longer side chains possess higher spherical symmetry compared to chains with lower side-chain lengths in contrast to what one may intuitively expect, as the stretching of the side chains is less important than the increase of their length. At higher temperatures, always below the Theta ($Θ$) temperature, coil-like configurations, similar to a single polymer chain, or brush-like configurations, similar to a homogeneous cylindrical bottle-brush polymer with a rigid backbone, are observed, depending on the choice of the particular parameters $N$ and $σ$. In the crossover regime between the collapsed state (globule) and the coil/brush regime the acylindricity increases, whereas for temperatures outside of this range, bottle-brush polymers maintain a highly cylindrical symmetry in all configurational states.

cond-mat.soft↗

arXiv2013

Universality in the three-dimensional random-field Ising model

We solve a long-standing puzzle in Statistical Mechanics of disordered systems. By performing a high-statistics simulation of the D=3 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute the complete set of critical exponents for this class, including the correction-to-scaling exponent, and we show, to high numerical accuracy, that scaling is described by two independent exponents. Discrepancies with previous works are explained in terms of strong scaling corrections.

cond-mat.dis-nn↗

arXiv2012

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 $n$ of alternating chemically different A and B blocks of the same length $N_{A}=N_{B}=N$. 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 $n$ can affect properties of the individual blocks, when chains are in a poor solvent for a certain range of $n$. 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.

cond-mat.soft↗

arXiv2010

Universality in disordered systems: The case of the three-dimensional random-bond Ising model

We study the critical behavior of the $d=3$ Ising model with bond randomness through extensive Monte Carlo simulations and finite-size scaling techniques. Our results indicate that the critical behavior of the random-bond model is governed by the same universality class as the site- and bond-diluted models, clearly distinct from that of the pure model, thus providing a complete set of universality in disordered systems.

cond-mat.stat-mech↗

arXiv2010

Microphase separation in linear multiblock copolymers under poor solvent conditions

Molecular dynamics simulations are used to study the phase behavior of linear multiblock copolymers with two types of monomers, A and B, where the length of the polymer blocks $N_{A}$ and $N_{B}$ ($N_{A}=N_{B}=N$), the number of the blocks $n_{A}$ and $n_{B}$ ($n_{A}=n_{B}=n$), and the solvent quality varies. The fraction $f$ of A-type monomers is kept constant and equal to 0.5. Whereas at high enough temperatures these macromolecules form coil structures, where each block A or B forms rather individual clusters, at low enough temperatures A and B monomers from different blocks can join together forming clusters of A or B monomers. The dependence of the formation of these clusters on the varied parameters is discussed in detail, providing a full understanding of the phase behavior of linear multiblock copolymers, at least for this symmetrical case.

cond-mat.soft↗

arXiv2010

Critical behavior of the pure and random-bond two-dimensional triangular Ising ferromagnet

We investigate the effects of quenched bond randomness on the critical properties of the two-dimensional ferromagnetic Ising model embedded in a triangular lattice. The system is studied in both the pure and disordered versions by the same efficient two-stage Wang-Landau method. In the first part of our study we present the finite-size scaling behavior of the pure model, for which we calculate the critical amplitude of the specific heat's logarithmic expansion. For the disordered system, the numerical data and the relevant detailed finite-size scaling analysis along the lines of the two well-known scenarios - logarithmic corrections versus weak universality - strongly support the field-theoretically predicted scenario of logarithmic corrections. A particular interest is paid to the sample-to-sample fluctuations of the random model and their scaling behavior that are used as a successful alternative approach to criticality.

cond-mat.stat-mech↗

arXiv2008

Universal features and tail analysis of the order-parameter distribution of the two-dimensional Ising model: An entropic sampling Monte Carlo study

We present a numerical study of the order-parameter probability density function (PDF) of the square Ising model for lattices with linear sizes $L=80-140$. A recent efficient entropic sampling scheme, combining the Wang-Landau and broad histogram methods and based on the high-levels of the Wang-Landau process in dominant energy subspaces is employed. We find that for large lattices there exists a stable window of the scaled order-parameter in which the full ansatz including the pre-exponential factor for the tail regime of the universal PDF is well obeyed. This window is used to estimate the equation of state exponent and to observe the behavior of the universal constants implicit in the functional form of the universal PDF. The probability densities are used to estimate the universal Privman-Fisher coefficient and to investigate whether one could obtain reliable estimates of the universal constants controlling the asymptotic behavior of the tail regime.

cond-mat.stat-mech↗

arXiv2008

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 $(\pmΔ)$ case and the model is studied on cubic lattices with sizes $4\leq L \leq 20$. 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.

cond-mat.stat-mech↗

arXiv2006

Lack of self-averaging of the specific heat in the three-dimensional random-field Ising model

We apply the recently developed critical minimum energy subspace scheme for the investigation of the random-field Ising model. We point out that this method is well suited for the study of this model. The density of states is obtained via the Wang-Landau and broad histogram methods in a unified implementation by employing the N-fold version of the Wang-Landau scheme. The random-fields are obtained from a bimodal distribution ($h_{i}=\pm2$), and the scaling of the specific heat maxima is studied on cubic lattices with sizes ranging from $L=4$ to $L=32$. Observing the finite-size scaling behavior of the maxima of the specific heats we examine the question of saturation of the specific heat. The lack of self-averaging of this quantity is fully illustrated and it is shown that this property may be related to the question mentioned above.

cond-mat.stat-mech↗

arXiv2005

The CrMES scheme as an alternative to Importance Sampling: The tail regime of the order-parameter distribution

We review the recently developed critical minimum energy-subspace (CrMES) technique. This scheme produces an immense optimization of popular algorithms, such as the Wang-Landau (WL) and broad histogram methods, by predicting the essential part of the energy space necessary for the estimation of the critical behavior and provides a new route of critical exponent estimation. A powerful and efficient CrMES entropic sampling scheme is proposed as an alternative to the traditional importance sampling methods. Utilizing the WL random walk process in the dominant energy subspace (CrMES-WL sampling) and using the WL approximation of the density of states and appropriate microcanonical estimators we determine the magnetic properties of the 2D Ising model. Updating $(E,M)$ histograms during the high level WL-iterations, we provide a comprehensive alternative scheme to the Metropolis algorithm and by applying this procedure we present a convincing analysis for the far tail regime of the order-parameter probability distribution.

cond-mat.stat-mech↗