arXiv subjects

Wolfhard Janke

Publications and source records attributed to Wolfhard Janke.

At least 91 records · Page 5Linked to original sources

arXiv2015

Macroscopic Degeneracy and order in the 3d plaquette Ising model

The purely plaquette 3d Ising Hamiltonian with the spins living at the vertices of a cubic lattice displays several interesting features. The symmetries of the model lead to a macroscopic degeneracy of the low-temperature phase and prevent the definition of a standard magnetic order parameter. Consideration of the strongly anisotropic limit of the model suggests that a layered, "fuki-nuke" order still exists and we confirm this with multicanonical simulations. The macroscopic degeneracy of the low-temperature phase also changes the finite-size scaling corrections at the first-order transition in the model and we see this must be taken into account when analysing our measurements.

cond-mat.stat-mech↗

arXiv2015

Knots as Topological Order Parameter For Semi-Flexible Polymers

Using a combination of the replica-exchange Monte Carlo algorithm and the multicanonical method, we investigate the influence of bending stiffness on the conformational phases of a bead-stick homopolymer model and present the pseudo-phase diagram for the complete range of semi-flexible polymers, from flexible to stiff. Although a simple model, we observe a rich variety of conformational phases, reminiscent of conformations observed for synthetic polymers or biopolymers. Changing the internal bending stiffness, the model exhibits different pseudo phases like bent, hairpin or toroidal. In particular, we find thermodynamically stable knots and transitions into these knotted phases with a clear phase coexistence, but almost no change in the mean total energy.

cond-mat.soft↗

arXiv2015

Open boundary conditions in stochastic transport processes with pair-factorized steady states

Using numerical methods we discuss the effects of open boundary conditions on condensation phenomena in the zero-range process (ZRP) and transport processes with pair-factorized steady states (PFSS), an extended model of the ZRP with nearest-neighbor interaction. For the zero-range process we compare to analytical results in the literature with respect to criticality and condensation. For the extended model we find a similar phase structure, but observe supercritical phases with droplet formation for strong boundary drives.

cond-mat.stat-mech↗

arXiv2015

Numerical survey of the tunable condensate shape and scaling laws in pair-factorized steady states

We numerically survey predictions on the shapes and scaling laws of particle condensates that emerge as a result of spontaneous symmetry breaking in pair- factorized steady states of a stochastic transport process. The specific model consists of indistinguishable particles that stochastically hop between sites controlled by a tunable potential. We identify the different condensate shapes within their respective parameter regimes as well as determine precisely the condensate width scaling.

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↗

arXiv2015

Planar ordering in the plaquette-only gonihedric Ising model

In this paper we conduct a careful multicanonical simulation of the isotropic $3d$ plaquette ("gonihedric") Ising model and confirm that a planar, fuki-nuke type order characterises the low-temperature phase of the model. From consideration of the anisotropic limit of the model we define a class of order parameters which can distinguish the low- and high-temperature phases in both the anisotropic and isotropic cases. We also verify the recently voiced suspicion that the order parameter like behaviour of the standard magnetic susceptibility $χ_m$ seen in previous Metropolis simulations was an artefact of the algorithm failing to explore the phase space of the macroscopically degenerate low-temperature phase. $χ_m$ is therefore not a suitable order parameter for the model.

cond-mat.stat-mech↗

arXiv2015

From amorphous aggregates to polymer bundles: The role of stiffness on structural phases in polymer aggregation

We study the aggregation transition of a finite theta-polymer system in dependence on the bending stiffness $κ$ with the help of parallel multicanonical simulations. In order to distinguish amorphous aggregates from polymer bundles we introduce an order parameter, measuring the correlation of the end-to-end vectors. With the help of this order parameter, we construct generic $T$-$κ$ phase diagrams for systems with $2$ and $8$ polymers and discuss the occurring phases from amorphous aggregates to bundle structures. For an intermediate stiffness range we find multiple aggregated phases which change with increasing number of polymers and discuss their nature with the help of microcanonical analyses. We show that the stiffness of semiflexible theta polymers is the distinguishing parameter for the emergent structural motifs.

cond-mat.soft↗

arXiv2015

First-order directional ordering transition in the three-dimensional compass model

We study the low-temperature properties of the classical three-dimensional compass or $t_{2g}$ orbital model on simple-cubic lattices by means of comprehensive large-scale Monte Carlo simulations. Our numerical results give evidence for a directionally ordered phase that is reached via a first-order transition at the temperature $T_0 = 0.098328(3) J / k_{\mathrm{B}}$. To obtain our results we employ local and cluster update algorithms, parallel tempering and multiple histogram reweighting as well as model-specific screw-periodic boundary conditions, which help counteract severe finite-size effects.

cond-mat.stat-mech↗

arXiv2014

Aggregation of theta-polymers in spherical confinement

We investigate the aggregation transition of theta polymers in spherical confinement with multicanonical simulations. This allows for a systematic study of the effect of density on the aggregation transition temperature for up to 24 monodisperse polymers. Our results for solutions in the dilute regime show that polymers can be considered isolated for all temperatures larger than the aggregation temperature, which is shown to be a function of the density. The resulting competition between single-polymer collapse and aggregation yields the lower temperature bound of the isolated chain approximation. We provide entropic and energetic arguments to describe the density dependence and finite-size effects of the aggregation transition for monodisperse solutions in finite systems. This allows us to estimate the aggregation transition temperature of dilute systems in a spherical cavity, using a few simulations of small, sufficiently dilute polymer systems.

cond-mat.soft↗

arXiv2014

Transmuted finite-size scaling at first-order phase transitions

It is known that fixed boundary conditions modify the leading finite-size corrections for an L^3 lattice in 3d at a first-order phase transition from 1/L^3 to 1/L. We note that an exponential low-temperature phase degeneracy of the form 2^3L will lead to a different leading correction of order 1/L^2 . A 3d gonihedric Ising model with a four-spin interaction, plaquette Hamiltonian displays such a degeneracy and we confirm the modified scaling behaviour using high-precision multicanonical simulations. We remark that other models such as the Ising antiferromagnet on the FCC lattice, in which the number of "true" low-temperature phases is not macroscopically large but which possess an exponentially degenerate number of low lying states may display an effective version of the modified scaling law for the range of lattice sizes accessible in simulations.

cond-mat.stat-mech↗

arXiv2014

Persistence-Length Renormalization of Polymers in a Crowded Environment of Hard Disks

The most conspicuous property of a semiflexible polymer is its persistence length, defined as the decay length of tangent correlations along its contour. Using an efficient stochastic growth algorithm to sample polymers embedded in a quenched two-dimensional hard-disk fluid, we find apparent wormlike chain statistics with a renormalized persistence length. We identify a universal form of the disorder renormalization that suggests itself as a quantitative measure of molecular crowding.

cond-mat.soft↗

arXiv2014

Asymptotic scaling behavior of self-avoiding walks on critical percolation clusters

We study self-avoiding walks on three-dimensional critical percolation clusters using a new exact enumeration method. It overcomes the exponential increase in computation time by exploiting the clusters' fractal nature. We enumerate walks of over $10^4$ steps, far more than has ever been possible. The scaling exponent $ν$ for the end-to-end distance turns out to be smaller than previously thought and appears to be the same on the backbones as on full clusters. We find strong evidence against the widely assumed scaling law for the number of conformations and propose an alternative, which perfectly fits our data.

cond-mat.stat-mech↗

arXiv2014

Multicanonical analysis of the plaquette-only gonihedric Ising model and its dual

The three-dimensional purely plaquette gonihedric Ising model and its dual are investigated to resolve inconsistencies in the literature for the values of the inverse transition temperature of the very strong temperature-driven first-order phase transition that is apparent in the system. Multicanonical simulations of this model allow us to measure system configurations that are suppressed by more than 60 orders of magnitude compared to probable states. With the resulting high-precision data, we find excellent agreement with our recently proposed nonstandard finite-size scaling laws for models with a macroscopic degeneracy of the low-temperature phase by challenging the prefactors numerically. We find an overall consistent inverse transition temperature of 0.551334(8) from the simulations of the original model both with periodic and fixed boundary conditions, and the dual model with periodic boundary conditions. For the original model with periodic boundary conditions, we obtain the first reliable estimate of the interface tension, 0.12037(18), using the statistics of suppressed configurations.

cond-mat.stat-mech↗

arXiv2014

Non-Standard Finite-Size Scaling at First-Order Phase Transitions

We note that the standard inverse system volume scaling for finite-size corrections at a first-order phase transition (i.e., 1/L^3 for an L x L x L lattice in 3D) is transmuted to 1/L^2 scaling if there is an exponential low-temperature phase degeneracy. The gonihedric Ising model which has a four-spin interaction, plaquette Hamiltonian provides an exemplar of just such a system. We use multicanonical simulations of this model to generate high-precision data which provides strong confirmation of the non-standard finite-size scaling law. The dual to the gonihedric model, which is an anisotropically coupled Ashkin-Teller model, has a similar degeneracy and also displays the non-standard scaling.

cond-mat.stat-mech↗

arXiv2014

Adsorption and Pattern Recognition of Polymers at Complex Surfaces with Attractive Stripe-like Motifs

We construct the complete structural phase diagram of polymer adsorption at substrates with attractive stripe-like patterns in the parameter space spanned by the adsorption affinity of the stripes and temperature. Results were obtained by extensive generalized-ensemble Monte Carlo simulations of a generic model for the hybrid organic-inorganic system. By comparing with adhesion properties at homogeneous substrates, we find substantial differences in the formation of adsorbed polymer structures if translational invariance at the surface is broken by a regular pattern. Beside a more specific understanding of polymer adsorption processes, our results are potentially relevant for the design of macromolecular pattern recognition devices such as sensors.

cond-mat.stat-mech↗

arXiv2014

Application of the parallel multicanonical method to lattice gas condensation

We present the speedup from a novel parallel implementation of the multicanonical method on the example of a lattice gas in two and three dimensions. In this approach, all cores perform independent equilibrium runs with identical weights, collecting their sampled histograms after each iteration in order to estimate consecutive weights. The weights are then redistributed to all cores. These steps are repeated until the weights are converged. This procedure benefits from a minimum of communication while distributing the necessary amount of statistics efficiently. Using this method allows us to study a broad temperature range for a variety of large and complex systems. Here, a gas is modeled as particles on the lattice, which interact only with their nearest neighbors. For a fixed density this model is equivalent to the Ising model with fixed magnetization. We compare our results to an analytic prediction for equilibrium droplet formation, confirming that a single macroscopic droplet forms only above a critical density.

cond-mat.stat-mech↗

arXiv2013

Scaling Properties of Parallelized Multicanonical Simulations

We implemented a parallel version of the multicanonical algorithm and applied it to a variety of systems with phase transitions of first and second order. The parallelization relies on independent equilibrium simulations that only communicate when the multicanonical weight function is updated. That way, the Markov chains efficiently sample the temporary distributions allowing for good estimations of consecutive weight functions. The systems investigated range from the well known Ising and Potts spin systems to bead-spring polymers. We estimate the speedup with increasing number of parallel processes. Overall, the parallelization is shown to scale quite well. In the case of multicanonical simulations of the $q$-state Potts model ($q\ge6$) and multimagnetic simulations of the Ising model, the optimal performance is limited due to emerging barriers.

physics.comp-ph↗

arXiv2013

Conformational transitions in random heteropolymer models

We study the conformational properties of heteropolymers containing two types of monomers A and B, modeled as self-avoiding random walks on a regular lattice. Such a model can describe in particular the sequences of hydrophobic and hydrophilic residues in proteins (K.F. Lau and K.A. Dill, Macromolecules {\bf 22}, 3986 (1989)) and polyampholytes with oppositely charged groups (Y. Kantor and M. Kardar, Europhys. Lett.{\bf 28}, 169 (1994)). Treating the sequences of the two types of monomers as quenched random variables, we provide a systematic analysis of possible generalizations of this model. To this end we apply the pruned-enriched Rosenbluth chain-growth algorithm (PERM), which allows us to obtain the phase diagrams of extended and compact states coexistence as function of both the temperature and fraction of A and B monomers along the heteropolymer chain.

cond-mat.dis-nn↗