arXiv subjects

Wolfhard Janke

Publications and source records attributed to Wolfhard Janke.

At least 145 records · Page 8Linked to original sources

arXiv2009

Comprehensive quantum Monte Carlo study of the quantum critical points in planar dimerized/quadrumerized Heisenberg models

We study two planar square lattice Heisenberg models with explicit dimerization or quadrumerization of the couplings in the form of ladder and plaquette arrangements. We investigate the quantum critical points of those models by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio $α= J^\prime/J$. The critical point of the order-disorder quantum phase transition in the ladder model is determined as $α_\mathrm{c} = 1.9096(2)$ improving on previous studies. For the plaquette model we obtain $α_\mathrm{c} = 1.8230(2)$ establishing a first benchmark for this model from quantum Monte Carlo simulations. Based on those values we give further convincing evidence that the models are in the three-dimensional (3D) classical Heisenberg universality class. The results of this contribution shall be useful as references for future investigations on planar Heisenberg models such as concerning the influence of non-magnetic impurities at the quantum critical point.

cond-mat.str-el↗

arXiv2008

Cross-correlations in scaling analyses of phase transitions

Thermal or finite-size scaling analyses of importance sampling Monte Carlo time series in the vicinity of phase transition points often combine different estimates for the same quantity, such as a critical exponent, with the intent to reduce statistical fluctuations. We point out that the origin of such estimates in the same time series results in often pronounced cross-correlations which are usually ignored even in high-precision studies, generically leading to significant underestimation of statistical fluctuations. We suggest to use a simple extension of the conventional analysis taking correlation effects into account, which leads to improved estimators with often substantially reduced statistical fluctuations at almost no extra cost in terms of computation time.

cond-mat.stat-mech↗

arXiv2008

Universal ratios of critical amplitudes in the Potts model universality class

Monte Carlo (MC) simulations and series expansions (SE) data for the energy, specific heat, magnetization, and susceptibility of the three-state and four-state Potts model and Baxter-Wu model on the square lattice are analyzed in the vicinity of the critical point in order to estimate universal combinations of critical amplitudes. We also form effective ratios of the observables close to the critical point and analyze how they approach the universal critical-amplitude ratios. In particular, using the duality relation, we show analytically that for the Potts model with a number of states $q\le 4$, the effective ratio of the energy critical amplitudes always approaches unity linearly with respect to the reduced temperature. This fact leads to the prediction of relations among the amplitudes of correction-to-scaling terms of the specific heat in the low- and high-temperature phases. It is a common belief that the four-state Potts and the Baxter-Wu model belong to the same universality class. At the same time, the critical behavior of the four-state Potts model is modified by logarithmic corrections while that of the Baxter-Wu model is not. Numerical analysis shows that critical amplitude ratios are very close for both models and, therefore, gives support to the hypothesis that the critical behavior of both systems is described by the same renormalization group fixed point.

cond-mat.stat-mech↗

arXiv2008

Evidence of Unconventional Universality Class in a Two-Dimensional Dimerized Quantum Heisenberg Model

The two-dimensional $J$-$J^\prime$ dimerized quantum Heisenberg model is studied on the square lattice by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio \hbox{$α=J^\prime/J$}. The critical point of the order-disorder quantum phase transition in the $J$-$J^\prime$ model is determined as \hbox{$α_\mathrm{c}=2.5196(2)$} by finite-size scaling for up to approximately $10 000$ quantum spins. By comparing six dimerized models we show, contrary to the current belief, that the critical exponents of the $J$-$J^\prime$ model are not in agreement with the three-dimensional classical Heisenberg universality class. This lends support to the notion of nontrivial critical excitations at the quantum critical point.

cond-mat.stat-mech↗

arXiv2008

Monte Carlo simulations of the directional-ordering transition in the two-dimensional classical and quantum compass model

A comprehensive study of the two-dimensional (2D) compass model on the square lattice is performed for classical and quantum spin degrees of freedom using Monte Carlo and quantum Monte Carlo methods. We employ state-of-the-art implementations using Metropolis, stochastic series expansion and parallel tempering techniques to obtain the critical ordering temperatures and critical exponents. In a pre-investigation we reconsider the classical compass model where we study and contrast the finite-size scaling behavior of ordinary periodic boundary conditions against annealed boundary conditions. It is shown that periodic boundary conditions suffer from extreme finite-size effects which might be caused by closed loop excitations on the torus. These excitations also appear to have severe effects on the Binder parameter. On this footing we report on a systematic Monte Carlo study of the quantum compass model. Our numerical results are at odds with recent literature on the subject which we trace back to neglecting the strong finite-size effects on periodic lattices. The critical temperatures are obtained as $T_\mathrm{c}=0.1464(2)J$ and $T_\mathrm{c}=0.055(1)J$ for the classical and quantum version, respectively, and our data support a transition in the 2D Ising universality class for both cases.

cond-mat.stat-mech↗

arXiv2008

Boundary field induced first-order transition in the 2D Ising model: numerical study

In a recent paper, Clusel and Fortin [J. Phys. A.: Math. Gen. 39 (2006) 995] presented an analytical study of a first-order transition induced by an inhomogeneous boundary magnetic field in the two-dimensional Ising model. They identified the transition that separates the regime where the interface is localized near the boundary from the one where it is propagating inside the bulk. Inspired by these results, we measured the interface tension by using multimagnetic simulations combined with parallel tempering to determine the phase transition and the location of the interface. Our results are in very good agreement with the theoretical predictions. Furthermore, we studied the spin-spin correlation function for which no analytical results are available.

cond-mat.stat-mech↗

arXiv2008

Make life simple: unleash the full power of the parallel tempering algorithm

We introduce a new update scheme to systematically improve the efficiency of parallel tempering simulations. We show that by adapting the number of sweeps between replica exchanges to the canonical autocorrelation time, the average round-trip time of a replica in temperature space can be significantly decreased. The temperatures are not dynamically adjusted as in previous attempts but chosen to yield a 50% exchange rate of adjacent replicas. We illustrate the new algorithm with results for the Ising model in two and the Edwards-Anderson Ising spin glass in three dimensions

cond-mat.stat-mech↗

arXiv2008

Walking on fractals: diffusion and self-avoiding walks on percolation clusters

We consider random walks (RWs) and self-avoiding walks (SAWs) on disordered lattices directly at the percolation threshold. Applying numerical simulations, we study the scaling behavior of the models on the incipient percolation cluster in space dimensions d=2, 3, 4. Our analysis yields estimates of universal exponents, governing the scaling laws for configurational properties of RWs and SAWs.

cond-mat.dis-nn↗

arXiv2008

Multifractality of self-avoiding walks on percolation clusters

We consider self-avoiding walks (SAWs) on the backbone of percolation clusters in space dimensions d=2, 3, 4. Applying numerical simulations, we show that the whole multifractal spectrum of singularities emerges in exploring the peculiarities of the model. We obtain estimates for the set of critical exponents, that govern scaling laws of higher moments of the distribution of percolation cluster sites visited by SAWs, in a good correspondence with an appropriately summed field-theoretical \varepsilon=6-d-expansion (H.-K. Janssen and O. Stenull, Phys. Rev. E 75, 020801(R) (2007)).

cond-mat.dis-nn↗

arXiv2008

Scaling behavior of self-avoiding walks on percolation clusters

The scaling behavior of self-avoiding walks (SAWs) on the backbone of percolation clusters in two, three and four dimensions is studied by Monte Carlo simulations. We apply the pruned-enriched Rosenbluth chain-growth method (PERM). Our numerical results bring about the estimates of critical exponents, governing the scaling laws of disorder averages of the end-to-end distance of SAW configurations. The effects of finite-size scaling are discussed as well.

cond-mat.dis-nn↗

arXiv2008

Percolation of Vortices in the 3D Abelian Lattice Higgs Model

The compact Abelian Higgs model is simulated on a cubic lattice where it possesses vortex lines and pointlike magnetic monopoles as topological defects. The focus of this high-precision Monte Carlo study is on the vortex network, which is investigated by means of percolation observables. In the region of the phase diagram where the Higgs and confinement phases are separated by a first-order transition, it is shown that the vortices percolate right at the phase boundary, and that the first-order nature of the transition is reflected by the network. In the crossover region, where the phase boundary ceases to be first order, the vortices are shown to still percolate. In contrast to other observables, the percolation observables show finite-size scaling. The exponents characterizing the critical behavior of the vortices in this region are shown to fall in the random percolation universality class.

hep-lat↗

arXiv2008

Geometric Properties of the Three-Dimensional Ising and XY Models

The fractal structure of high-temperature graphs of the three-dimensional Ising and XY models is investigated by simulating these graphs directly on a cubic lattice and analyzing them with the help of percolation observables. The Ising graphs are shown to percolate right at the Curie critical point. The diverging length scale relevant to the graphs in the vicinity of the percolation threshold is shown to be provided by the spin correlation length. The fractal dimension of the high-temperature graphs at criticality is estimated to be $D = 1.7349(65)$ for the Ising and $D = 1.7626(66)$ for the XY model.

cond-mat.stat-mech↗

arXiv2007

Thermodynamics and Kinetics of a Go Proteinlike Heteropolymer Model with Two-State Folding Characteristics

We present results of Monte Carlo computer simulations of a coarse-grained hydrophobic-polar Go-like heteropolymer model and discuss thermodynamic properties and kinetics of an exemplified heteropolymer, exhibiting two-state folding behavior. It turns out that general, characteristic folding features of realistic proteins with a single free-energy barrier can also be observed in this simplified model, where the folding transition is primarily driven by the hydrophobic force.

cond-mat.soft↗

arXiv2007

Thermodynamics of Peptide Aggregation Processes. An Analysis from Perspectives of Three Statistical Ensembles

We employ a mesoscopic model for studying aggregation processes of protein-like hydrophobic-polar heteropolymers. By means of multicanonical Monte Carlo computer simulations, we find strong indications that peptide aggregation is a phase separation process, in which the microcanonical entropy exhibits a convex intruder due to nonnegligible surface effects of the small systems. We analyze thermodynamic properties of the conformational transitions accompanying the aggregation process from the multicanonical, canonical, and microcanonical perspective. It turns out that the microcanonical description is particularly advantageous as it allows for unraveling details of the phase-separation transition in the thermodynamic region, where the temperature is not a suitable external control parameter anymore.

cond-mat.soft↗

arXiv2007

Differences in Solution Behavior among Four Semiconductor-Binding Peptides

Recent experiments have identified peptides with adhesion affinity for GaAs and Si surfaces. Here we use all-atom Monte Carlo (MC) simulations with implicit solvent to investigate the behavior in aqueous solution of four such peptides, all with 12 residues. At room temperature, we find that all the four peptides are largely unstructured, which is consistent with experimental data. At the same time, we find that one of the peptides is structurally different and more flexible, compared to the others. This finding points at structural differences as a possible explanation for differences in adhesion properties between these peptides. By also analyzing designed mutants of two of the peptides, an experimental test of this hypothesis is proposed.

cond-mat.soft↗

arXiv2007

Phase Separation in Peptide Aggregation Processes - Multicanonical Study of a Mesoscopic Model

We have performed multicanonical computer simulations of a small system of short protein-like heteropolymers and found that their aggregation transition possesses similarities to first-order phase separation processes. Not being a phase transition in the thermodynamic sense, the observed folding-binding behavior exhibits fascinating features leading to the conclusion that the temperature is no suitable control parameter in the transition region. More formally, for such small systems the microcanonical interpretation is more favorable than the typically used canonical picture.

cond-mat.soft↗

arXiv2007

Thermodynamics of Protein Folding from Coarse-Grained Models' Perspectives

Folding and aggregation of proteins, the interaction between proteins and membranes, as well as the adsorption of organic soft matter to inorganic solid substrates belong to the most interesting challenges in understanding structure and function of complex macromolecules. This is reasoned by the interdisciplinary character of the associated questions ranging from the molecular origin of the loss of biological functionality as, for example, in Alzheimer's disease to the development of organic circuits for biosensory applications. In this lecture, we focus on the analysis of mesoscopic models for protein folding, aggregation, and hybrid systems of soft and solid condensed matter. The simplicity of the coarse-grained models allows for a more universal description of the notoriously difficult problem of protein folding. In this approach, classifications of structure formation processes with respect to the conformational pseudophases are possible. This is similar in aggregation and adsorption processes, where the individual folding propensity is influenced by external forces. The main problem in studies of conformational transitions is that the sequences of amino acids proteins are built up of are necessarily of finite length and, therefore, a thermodynamic limit does not exist. Thus, structural transitions are not phase transitions in the strict thermodynamic sense and the analysis of pseudouniversal aspects is intricate, as apparently small-system effects accompany all conformational transitions and cannot be neglected.

cond-mat.soft↗

arXiv2007

Identification of Characteristic Protein Folding Channels in a Coarse-Grained Hydrophobic-Polar Peptide Model

Folding channels and free-energy landscapes of hydrophobic-polar heteropolymers are discussed on the basis of a minimalistic off-lattice coarse-grained model. We investigate how rearrangements of hydrophobic and polar monomers in a heteropolymer sequence lead to completely different folding behaviors. Studying three exemplified sequences with the same content of hydrophobic and polar residues, we can reproduce within this simple model two-state folding, folding through intermediates, as well as metastability.

cond-mat.soft↗