arXiv subjects

Wolfhard Janke

Publications and source records attributed to Wolfhard Janke.

At least 127 records · Page 7Linked to original sources

arXiv2010

Critical amplitude ratios of the Baxter-Wu model

A Monte Carlo simulation study of the critical and off-critical behavior of the Baxter-Wu model, which belongs to the universality class of the 4-state Potts model, was performed. We estimate the critical temperature window using known analytical results for the specific heat and magnetization. This helps us to extract reliable values of universal combinations of critical amplitudes with reasonable accuracy. Comparisons with approximate analytical predictions and other numerical results are discussed.

cond-mat.stat-mech↗

arXiv2010

Re-examining the directional-ordering transition in the compass model with screw-periodic boundary conditions

We study the directional-ordering transition in the two-dimensional classical and quantum compass models on the square lattice by means of Monte Carlo simulations. An improved algorithm is presented which builds on the Wolff cluster algorithm in one-dimensional subspaces of the configuration space. This improvement allows us to study classical systems up to $L=512$. Based on the new algorithm we give evidence for the presence of strongly anomalous scaling for periodic boundary conditions which is much worse than anticipated before. We propose and study alternative boundary conditions for the compass model which do not make use of extended configuration spaces and show that they completely remove the problem with finite-size scaling. In the last part, we apply these boundary conditions to the quantum problem and present a considerably improved estimate for the critical temperature which should be of interest for future studies on the compass model. Our investigation identifies a strong one-dimensional magnetic ordering tendency with a large correlation length as the cause of the unusual scaling and moreover allows for a precise quantification of the anomalous length scale involved.

cond-mat.stat-mech↗

arXiv2010

Error estimation and reduction with cross correlations

Besides the well-known effect of autocorrelations in time series of Monte Carlo simulation data resulting from the underlying Markov process, using the same data pool for computing various estimates entails additional cross correlations. This effect, if not properly taken into account, leads to systematically wrong error estimates for combined quantities. Using a straightforward recipe of data analysis employing the jackknife or similar resampling techniques, such problems can be avoided. In addition, a covariance analysis allows for the formulation of optimal estimators with often significantly reduced variance as compared to more conventional averages.

cond-mat.stat-mech↗

arXiv2010

Holographic interpretation of two-dimensional O(N) models coupled to quantum gravity

Various two-dimensional O(N) models coupled to Euclidean quantum gravity, whose intrinsic dimension is four, are shown to belong to universality classes of nongravitating statistical models in a lower number of dimensions. It is speculated that the matching critical behaviors in the gravitating and dimensionally reduced models may be manifestations of the holographic principle.

cond-mat.stat-mech↗

arXiv2010

Surface effects in the crystallization process of elastic flexible polymers

Investigating thermodynamic properties of liquid-solid transitions of flexible homopolymers with elastic bonds by means of multicanonical Monte Carlo simulations, we find crystalline conformations that resemble ground-state structures of Lennard-Jones clusters. This allows us to set up a structural classification scheme for finite-length flexible polymers and their freezing mechanism in analogy to atomic cluster formation. Crystals of polymers with "magic length" turn out to be perfectly icosahedral.

cond-mat.soft↗

arXiv2010

Critical Loop Gases and the Worm Algorithm

The loop gas approach to lattice field theory provides an alternative, geometrical description in terms of fluctuating loops. Statistical ensembles of random loops can be efficiently generated by Monte Carlo simulations using the worm update algorithm. In this paper, concepts from percolation theory and the theory of self-avoiding random walks are used to describe estimators of physical observables that utilize the nature of the worm algorithm. The fractal structure of the random loops as well as their scaling properties are studied. To support this approach, the O(1) loop model, or high-temperature series expansion of the Ising model, is simulated on a honeycomb lattice, with its known exact results providing valuable benchmarks.

cond-mat.stat-mech↗

arXiv2010

Ground-state properties of tubelike flexible polymers

In this work we investigate structural properties of native states of a simple model for short flexible homopolymers, where the steric influence of monomeric side chains is effectively introduced by a thickness constraint. This geometric constraint is implemented through the concept of the global radius of curvature and affects the conformational topology of ground-state structures. A systematic analysis allows for a thickness-dependent classification of the dominant ground-state topologies. It turns out that helical structures, strands, rings, and coils are natural, intrinsic geometries of such tubelike objects.

cond-mat.soft↗

arXiv2010

Systematic Microcanonical Analyses of Polymer Adsorption Transitions

In detailed microcanonical analyses of densities of states obtained by extensive multicanonical Monte Carlo computer simulations, we investigate the caloric properties of conformational transitions adsorbing polymers experience near attractive substrates. For short chains and strong surface attraction, the microcanonical entropy turns out to be a convex function of energy in the transition regime, indicating that surface-entropic effects are relevant. Albeit known to be a continuous transition in the thermodynamic limit of infinitely long chains, the adsorption transition of nongrafted finite-length polymers thus exhibits a clear signature of a first-order-like transition, with coexisting phases of adsorbed and desorbed conformations. Another remarkable consequence of the convexity of the microcanonical entropy is that the transition is accompanied by a decrease of the microcanonical temperature with increasing energy. Since this is a characteristic physical effect it might not be ignored in analyses of cooperative macrostate transitions in finite systems.

cond-mat.stat-mech↗

arXiv2009

Finite-Temperature Néel Ordering of Fluctuations in a Plaquette Orbital Model

We present a pseudospin model which should be experimentally accessible using solid-state devices and, being a variation on the compass model, adds to the toolbox for the protection of qubits in the area of quantum information. Using Monte Carlo methods, we find for both classical and quantum spins in two and three dimensions Ising-type Neel ordering of energy fluctuations at finite temperatures without magnetic order. We also readdress the controversy concerning the stability of the ordered state in the presence of quenched impurities and present numerical results which are at clear variance with earlier claims in the literature.

cond-mat.stat-mech↗

arXiv2009

Conformational Mechanics of Polymer Adsorption Transitions at Attractive Substrates

Conformational phases of a semiflexible off-lattice homopolymer model near an attractive substrate are investigated by means of multicanonical computer simulations. In our polymer-substrate model, nonbonded pairs of monomers as well as monomers and the substrate interact via attractive van der Waals forces. To characterize conformational phases of this hybrid system, we analyze thermal fluctuations of energetic and structural quantities, as well as adequate docking parameters. Introducing a solvent parameter related to the strength of the surface attraction, we construct and discuss the solubility-temperature phase diagram. Apart from the main phases of adsorbed and desorbed conformations, we identify several other phase transitions such as the freezing transition between energy-dominated crystalline low-temperature structures and globular entropy-dominated conformations.

physics.comp-ph↗

arXiv2009

Thermodynamics of tubelike flexible polymers

In this work we present the general phase behavior of short tubelike flexible polymers. The geometric thickness constraint is implemented through the concept of the global radius of curvature. We use sophisticated Monte Carlo sampling methods to simulate small bead-stick polymer models with Lennard-Jones interaction among non-bonded monomers. We analyze energetic fluctuations and structural quantities to classify conformational pseudophases. We find that the tube thickness influences the thermodynamic behavior of simple tubelike polymers significantly, i.e., for given temperature, the formation of secondary structures strongly depends on the tube thickness.

cond-mat.soft↗

arXiv2009

Anisotropy of the interface tension of the three-dimensional Ising model

We determine the interface tension for the 100, 110 and 111 interface of the simple cubic Ising model with nearest-neighbour interaction using novel simulation methods. To overcome the droplet/strip transition and the droplet nucleation barrier we use a newly developed combination of the multimagnetic algorithm with the parallel tempering method. We investigate a large range of inverse temperatures to study the anisotropy of the interface tension in detail.

cond-mat.stat-mech↗

arXiv2009

Conformational Transitions in Molecular Systems

Proteins are the "work horses" in biological systems. In almost all functions specific proteins are involved. They control molecular transport processes, stabilize the cell structure, enzymatically catalyze chemical reactions; others act as molecular motors in the complex machinery of molecular synthetization processes. Due to their significance, misfolds and malfunctions of proteins typically entail disastrous diseases, such as Alzheimer's disease and bovine spongiform encephalopathy (BSE). Therefore, the understanding of the trinity of amino acid composition, geometric structure, and biological function is one of the most essential challenges for the natural sciences. Here, we glance at conformational transitions accompanying the structure formation in protein folding processes.

cond-mat.stat-mech↗

arXiv2009

Different Kinds of Protein Folding Identified with a Coarse-Grained Heteropolymer Model

Applying multicanonical simulations we investigated folding properties of off-lattice heteropolymers employing a mesoscopic hydrophobic-polar model. We study for various sequences folding channels in the free-energy landscape by comparing the equilibrium conformations with the folded state in terms of an angular overlap parameter. Although all investigated heteropolymer sequences contain the same content of hydrophobic and polar monomers, our analysis of the folding channels reveals a variety of characteristic folding behaviors known from realistic peptides.

cond-mat.soft↗

arXiv2009

Freezing and collapse of flexible polymers

We analyze the freezing and collapse transition of a simple model for flexible polymer chains on simple cubic and face-centered cubic lattices by means of sophisticated chain-growth methods. In contrast to bond-fluctuation polymer models in certain parameter ranges, where these two conformational transitions were found to merge in the thermodynamic limit, we conclude from our results that the two transitions remain well-separated in the limit of infinite chain lengths. The reason for this qualitatively distinct behavior is presumably due to the ultrashort attractive interaction range in the lattice models considered here.

cond-mat.soft↗

arXiv2009

Comparative Molecular Dynamics and Monte Carlo Study of Statistical Properties for Coarse-Grained Heteropolymers

Employing a simple hydrophobic-polar heteropolymer model, we compare thermodynamic quantities obtained from Andersen and Nose-Hoover molecular dynamics as well as replica-exchange Monte Carlo methods. We find qualitative correspondence in the results, but serious quantitative differences using the Nose-Hoover chain thermostat. For analyzing the deviations, we study different parameterizations of the Nose-Hoover chain thermostat. Autocorrelations from molecular dynamics and Metropolis Monte Carlo runs are also investigated.

cond-mat.stat-mech↗

arXiv2009

Mesoscopic Properties of Molecular Folding and Aggregation Processes

Protein folding, peptide aggregation and crystallization, as well as adsorption of molecules on soft or solid substrates have an essential feature in common: In all these processes, structure formation is guided by a collective, cooperative behavior of the molecular subunits lining up to build chainlike macromolecules. Proteins experience conformational transitions related to thermodynamic phase transitions. For chains of finite length, an important difference of crossovers between conformational (pseudo)phases is, however, that these transitions are typically rather smooth processes, i.e., thermodynamic activity is not necessarily signalized by strong entropic or energetic fluctuations. Nonetheless, in order to understand generic properties of molecular structure-formation processes, the analysis of mesoscopic models from a statistical physics point of view enables first insights into the nature of conformational transitions in small systems. Here, we review recent results obtained by means of sophisticated generalized-ensemble computer simulations of minimalistic coarse-grained models.

cond-mat.stat-mech↗

arXiv2009

Thickness-dependent secondary structure formation of tubelike polymers

By means of sophisticated Monte Carlo methods, we investigate the conformational phase diagram of a simple model for flexible polymers with explicit thickness. The thickness constraint, which is introduced geometrically via the global radius of curvature of a polymer conformation, accounts for the excluded volume of the polymer and induces cooperative effects supporting the formation of secondary structures. In our detailed analysis of the temperature and thickness dependence of the conformational behavior for classes of short tubelike polymers, we find that known secondary-structure segments like helices and turns, but also ringlike conformations and stiff rods are dominant intrinsic topologies governing the phase behavior of such cooperative tubelike objects. This shows that the thickness constraint is indeed a fundamental physical parameter that allows for a classification of generic polymer structures.

cond-mat.soft↗