arXiv subjects

W. Janke

Publications and source records attributed to W. Janke.

At least 19 recordsLinked to original sources

arXiv2024

Entropic force in a dilute solution of real ring polymer chains with different topological structures in a slit of two parallel walls with mixed boundary conditions

The molecular dynamics simulations were used to obtain the radius of gyration of real ring polymer chains with different topological structures consisting of 360 monomers. We focus on the entropic force which is exerted by a dilute solution of ring polymer chains of different topological structures with the excluded volume interaction (EVI) in a good solvent on the confining parallel walls of a slit geometry. We consider mixed boundary conditions of one repulsive wall and the other one at the adsorption threshold. The obtained molecular dynamics simulation results for a wide slit region demonstrate a qualitative agreement with previous analytical results for ideal ring polymers. These results could lead to interesting potential applications in materials engineering and improve understanding of some biological processes suggested in the paper. Additionally, they could be applied in micro- and nano-electromechanical devices (MEMS and NEMS) in order to reduce the static friction.

cond-mat.soft↗

arXiv2024

Optimized population Monte Carlo

Population Monte Carlo simulations in the form commonly referred to as population annealing can serve as a useful meta-algorithm for simulating systems with complex free-energy landscapes. In the present paper we provide an easily accessible introduction to the approach, focusing on spin systems as simple example problems. While the method is very general and powerful, it also comes with a number of tunable parameters. Here, we discuss the question of an optimal choice of resampling protocol, that is shown to have significant influence on the quality of results. While population annealing is an excellent fit to the paradigm of massively parallel simulations, limitations in the availability of parallel resources and especially memory can provide a bottleneck to its efficacy. As we demonstrate for results of the Ising ferromagnetic and spin-glass models, weighted averages of smaller-scale runs can be easily combined to reduce both systematic and statistical errors in order to avoid such bottlenecks.

cond-mat.stat-mech↗

arXiv2023

Temperature scaling analysis of the 3D disordered Ising model with power-law correlated defects

We consider the three-dimensional site-diluted Ising model with power-law correlated defects and study the critical behavior of the second-moment correlation length and the magnetic susceptibility in the high-temperature phase. By comparing, for various defect correlation strengths, the extracted critical exponents $\nu$ and $\gamma$ with the results of our previous finite-size scaling study, we consolidate the exponent estimates.

cond-mat.stat-mech↗

arXiv2018

Universality from disorder in the random-bond Blume-Capel model

Using high-precision Monte Carlo simulations and finite-size scaling we study the effect of quenched disorder in the exchange couplings on the Blume-Capel model on the square lattice. The first-order transition for large crystal-field coupling is softened to become continuous, with a divergent correlation length. An analysis of the scaling of the correlation length as well as the susceptibility and specific heat reveals that it belongs to the universality class of the Ising model with additional logarithmic corrections observed for the Ising model itself if coupled to weak disorder. While the leading scaling behavior in the disordered system is therefore identical between the second-order and first-order segments of the phase diagram of the pure model, the finite-size scaling in the ex-first-order regime is affected by strong transient effects with a crossover length scale $L^{\ast} \approx 32$ for the chosen parameters.

cond-mat.dis-nn↗

arXiv2017

Scaling laws for random walks in long-range correlated disordered media

We study the scaling laws of diffusion in two-dimensional media with long-range correlated disorder through exact enumeration of random walks. The disordered medium is modelled by percolation clusters with correlations decaying with the distance as a power law, $r^{-a}$, generated with the improved Fourier filtering method. To characterize this type of disorder, we determine the percolation threshold $p_{\text c}$ by investigating cluster-wrapping probabilities. At $p_{\text c}$, we estimate the (sub-diffusive) walk dimension $d_{\text w}$ for different correlation exponents $a$. Above $p_{\text c}$, our results suggest a normal random walk behavior for weak correlations, whereas anomalous diffusion cannot be ruled out in the strongly correlated case, i.e., for small $a$.

cond-mat.stat-mech↗

arXiv2016

Scaling and universality in the phase diagram of the 2D Blume-Capel model

We review the pertinent features of the phase diagram of the zero-field Blume-Capel model, focusing on the aspects of transition order, finite-size scaling and universality. In particular, we employ a range of Monte Carlo simulation methods to study the 2D spin-1 Blume-Capel model on the square lattice to investigate the behavior in the vicinity of the first-order and second-order regimes of the ferromagnet-paramagnet phase boundary, respectively. To achieve high-precision results, we utilize a combination of (i) a parallel version of the multicanonical algorithm and (ii) a hybrid updating scheme combining Metropolis and generalized Wolff cluster moves. These techniques are combined to study for the first time the correlation length of the model, using its scaling in the regime of second-order transitions to illustrate universality through the observed identity of the limiting value of $ξ/L$ with the exactly known result for the Ising universality class.

cond-mat.stat-mech↗

arXiv2014

Polymers in disordered environments

A brief review of our recent studies aiming at a better understanding of the scaling behaviour of polymers in disordered environments is given. The main emphasis is on a simple generic model where the polymers are represented by (interacting) self-avoiding walks and the disordered environment by critical percolation clusters. The scaling behaviour of the number of conformations and their average spatial extent as a function of the number of monomers and the associated critical exponents $γ$ and $ν$ are examined with two complementary approaches: numerical chain-growth computer simulations using the PERM algorithm and complete enumerations of all possible polymer conformations employing a recently developed very efficient exact counting method.

cond-mat.soft↗

arXiv2013

Crossover scaling in the two-dimensional three-state Potts model

We apply simulated tempering and magnetizing (STM) Monte Carlo simulations to the two-dimensional three-state Potts model in an external magnetic field in order to investigate the crossover scaling behaviour in the temperature-field plane at the Potts critical point and towards the Ising universality class for negative magnetic fields. Our data set has been generated by STM simulations of several square lattices with sizes up to 160 x 160 spins, supplemented by conventional canonical simulations of larger lattices at selected simulation points. We present careful scaling and finite-size scaling analyses of the crossover behaviour with respect to temperature, magnetic field and lattice size.

cond-mat.stat-mech↗

arXiv2012

Simple flexible polymers in a spherical cage

We report the results of Monte Carlo simulations investigating the effect of a spherical confinement within a simple model for a flexible homopolymer. We use the parallel tempering method combined with multi-histogram reweighting analysis and multicanonical simulations to investigate thermodynamical observables over a broad range of temperatures, which enables us to describe the behavior of the polymer and to locate the freezing and collapse transitions. We find a strong effect of the spherical confinement on the location of the collapse transition, whereas the freezing transition is hardly effected.

cond-mat.soft↗

arXiv2010

Geometrothermodynamics of the Kehagias-Sfetsos Black Hole

The application of information geometric ideas to statistical mechanics using a metric on the space of states, pioneered by Ruppeiner and Weinhold, has proved to be a useful alternative approach to characterizing phase transitions. Some puzzling anomalies become apparent, however, when these methods are applied to the study of black hole thermodynamics. A possible resolution was suggested by Quevedo et al. who emphasized the importance of Legendre invariance in thermodynamic metrics. They found physically consistent results for various black holes when using a Legendre invariant metric, which agreed with a direct determination of the properties of phase transitions from the specific heat. Recently, information geometric methods have been employed by Wei et al. to study the Kehagias-Sfetsos (KS) black hole in Horava-Lifshitz gravity. The formalism suggests that a coupling parameter in this theory plays a role analogous to the charge in Reissner-Nordstrom (RN) black holes or angular momentum in the Kerr black hole and calculation of the specific heat shows a singularity which may be interpreted as a phase transition. When the curvature of the Ruppeiner metric is calculated for such a theory it does not, however, show a singularity at the phase transition point. We show that the curvature of a particular Legendre invariant ("Quevedo") metric for the KS black hole is singular at the phase transition point. We contrast the results for the Ruppeiner, Weinhold and Quevedo metrics and in the latter case investigate the consistency of taking either the entropy or mass as the thermodynamic potential.

hep-th↗

arXiv2010

Fractals Meet Fractals: Self-Avoiding Random Walks on Percolation Clusters

The scaling behavior of linear polymers in disordered media, modelled by self-avoiding walks (SAWs) on the backbone of percolation clusters in two, three and four dimensions is studied by numerical simulations. We apply the pruned-enriched Rosenbluth chain-growth method (PERM). Our numerical results yield estimates of critical exponents, governing the scaling laws of disorder averages of the configurational properties of SAWs, and clearly indicate a multifractal spectrum which emerges when two fractals meet each other.

cond-mat.dis-nn↗

arXiv2009

Mass condensation in one dimension with pair-factorized steady states

We consider stochastic rules of mass transport which lead to steady states that factorize over the links of a one-dimensional ring. Based on the knowledge of the steady states, we derive the onset of a phase transition from a liquid to a condensed phase that is characterized by the existence of a condensate. For various types of weight functions which enter the hopping rates, we determine the shape of the condensate, its scaling with the system size, and the single-site mass distribution as characteristic static properties. As it turns out, the condensate's shape and its scaling are not universal, but depend on the competition between local and ultralocal interactions. So we can tune the shape from a delta-like envelope to a parabolic-like or a rectangular one. While we treat the liquid phase in the grand-canonical formalism, we develop a different analytical approach for the condensed phase. Its predictions are well confirmed by numerical simulations. Possible extensions to higher dimensions are indicated.

cond-mat.stat-mech↗

arXiv2009

Polymers in crowded environment under stretching force: globule-coil transitions

We study flexible polymer macromolecules in a crowded (porous) environment, modelling them as self-attracting self-avoiding walks (SASAW) on site-diluted percolative lattices in space dimensions d=2, 3. The influence of stretching force on the polymer folding and properties of globule-coil transitions are analyzed. Applying the pruned-enriched Rosenbluth chain-growth method (PERM), we estimate the transition temperature T_Θ between collapsed and extended polymer configurations and construct the phase diagrams of the globule-coil coexistence when varying temperature and stretching force. The transition to a completely stretched state, caused by applying force, is discussed as well.

cond-mat.soft↗

arXiv2009

Tuning the shape of the condensate in spontaneous symmetry breaking

We investigate what determines the shape of a particle condensate in situations when it emerges as a result of spontaneous breaking of translational symmetry. We consider a model with particles hopping between sites of a one-dimensional grid and interacting if they are at the same or at neighboring nodes. We predict the envelope of the condensate and the scaling of its width with the system size for various interaction potentials and show how to tune the shape from a delta-peak to a rectangular or a parabolic-like form.

cond-mat.stat-mech↗

arXiv2009

Continued Fractions and the Partially Asymmetric Exclusion Process

We note that a tridiagonal matrix representation of the algebra of the partially asymmetric exclusion process (PASEP) lends itself to interpretation as the transfer matrix for weighted Motzkin lattice paths. A continued fraction ("J-Fraction") representation of the lattice path generating function is particularly well suited to discussing the PASEP, for which the paths have height dependent weights. We show that this not only allows a succinct derivation of the normalisation and correlation lengths of the PASEP, but also reveals how finite-dimensional representations of the PASEP algebra, valid only along special lines in the phase diagram, relate to the general solution that requires an infinite-dimensional representation.

cond-mat.stat-mech↗

arXiv2009

Pair-factorized steady states on arbitrary graphs

Stochastic mass transport models are usually described by specifying hopping rates of particles between sites of a given lattice, and the goal is to predict the existence and properties of the steady state. Here we ask the reverse question: given a stationary state that factorizes over links (pairs of sites) of an arbitrary connected graph, what are possible hopping rates that converge to this state? We define a class of hopping functions which lead to the same steady state and guarantee current conservation but may differ by the induced current strength. For the special case of anisotropic hopping in two dimensions we discuss some aspects of the phase structure. We also show how this case can be traced back to an effective zero-range process in one dimension which is solvable for a large class of hopping functions.

cond-mat.stat-mech↗

arXiv2008

Approaching the thermodynamic limit in equilibrated scale-free networks

We discuss how various models of scale-free complex networks approach their limiting properties when the size N of the network grows. We focus mainly on equilibrated networks and their finite-size degree distributions. Our results show that subleading corrections to the scaling of the position of the cutoff are strong even for networks of order 10^9 nodes. We observe also a logarithmic correction to the scaling for degenerated graphs when the degree distribution follows a power law k^(-3). We study also the distribution of the maximal degree and show that it may have a different scaling than the cutoff and, moreover, it approaches the thermodynamic limit much faster. We present also some results on the cutoff function and the distribution of the maximal degree in equilibrated networks.

cond-mat.stat-mech↗

arXiv2008

Thermodynamics of Heisenberg ferromagnets with arbitrary spin in a magnetic field

The thermodynamic properties (magnetization, magnetic susceptibility, transverse and longitudinal correlation lengths, specific heat) of one- and two-dimensional ferromagnets with arbitrary spin S in a magnetic field are investigated by a second-order Green-function theory. In addition, quantum Monte Carlo simulations for S= 1/2 and S=1 are performed using the stochastic series expansion method. A good agreement between the results of both approaches is found. The field dependence of the position of the maximum in the temperature dependence of the susceptibility fits well to a power law at low fields and to a linear increase at high fields. The maximum height decreases according to a power law in the whole field region. The longitudinal correlation length may show an anomalous temperature dependence: a minimum followed by a maximum with increasing temperature. Considering the specific heat in one dimension and at low magnetic fields, two maxima in its temperature dependence for both the S= 1/2 and S = 1 ferromagnets are found. For S>1 only one maximum occurs, as in the two-dimensional ferromagnets. Relating the theory to experiments on the S= 1/2 quasi-one-dimensional copper salt TMCuC [(CH_3)_4NCuCl_3], a fit to the magnetization as a function of the magnetic field yields the value of the exchange energy which is used to make predictions for the occurrence of two maxima in the temperature dependence of the specific heat.

cond-mat.str-el↗