arXiv subjects

Stefan Schnabel

Publications and source records attributed to Stefan Schnabel.

At least 19 recordsLinked to original sources

arXiv2023

Collapse transition of a Lennard Jones polymer

Using the recently introduced parsimonious Metropolis algorithm bead-stick polymers both with infinite-range Lennard-Jones interaction and with truncation are simulated. The focus lays on determining the Boyle temperature for long chains with thousands of repeat units and on testing for theoretically predicted logarithmic corrections. Subsequently the behavior at the infinite-chain transition temperature, i.e., the $Θ$-temperature is studied for chains with up to $N = 32768$ repeat units by investigation of the scaling of the end-to-end distance, the radius of gyration, the specific heat, and their derivatives with $N$.

cond-mat.soft↗

arXiv2023

Surveying an Energy Landscape

We derive a formula that expresses the density of states of a system with continuous degrees of freedom as a function of microcanonical averages of squared gradient and Laplacian of the Hamiltonian. This result is then used to propose a novel flat-histogram Monte Carlo algorithm, which is tested on a three-dimensional system of interacting Lennard-Jones particles, the O(n) vector spin model on hypercubic lattices in D = 1 to 5 dimensions, and the O(3) Heisenberg model on a triangular lattice featuring frustration effects.

cond-mat.stat-mech↗

arXiv2023

Monte Carlo Simulation of Long Hard-Sphere Polymer Chains in Two to Five Dimensions

We perform simulations for long hard-sphere polymer chains using a recently developed binary-tree based Monte Carlo method. Systems in two to five dimensions with free and periodic boundary conditions and up to $10^7$ repeat units are considered. We focus on the scaling properties of the end-to-end distance and on the entropy and their dependence on the sphere diameter. To this end new methods for measuring entropy and its derivatives are introduced. By determining the Flory exponent $ν$ and the weakly universal amplitude ratio of end-to-end distance to radius of gyration we find that the system generally reproduces the behavior of self-avoiding lattice walks in strong support of universality.

cond-mat.soft↗

arXiv2022

Fast, hierarchical, and adaptive algorithm for Metropolis Monte Carlo simulations of long-range interacting systems

We present a fast, hierarchical, and adaptive algorithm for Metropolis Monte Carlo simulations of systems with long-range interactions that reproduces the dynamics of a standard implementation exactly, i.e., the generated configurations and consequently all measured observables are identical, allowing in particular for nonequilibrium studies. The method is demonstrated for the power-law interacting long-range Ising model with nonconserved order parameter and a Lennard-Jones system both in two dimensions. The measured runtimes support an average complexity $O(N\log N)$, where $N$ is the number of spins or particles. Importantly, prefactors of this scaling behavior are small, which in practice manifests in speedup factors larger than $10^4$. The method is general and will allow the treatment of large systems that were out of reach before, likely enabling a more detailed understanding of physical phenomena rooted in long-range interactions.

physics.comp-ph↗

arXiv2022

Wang-Landau simulations with non-flat distributions

We show how the well-known Wang-Landau method can be modified to produce non-flat distributions. Through the choice of a suitable profile this can lead to an increase in efficiency for some systems. Examples for such an enhancement are provided.

physics.comp-ph↗

arXiv2022

A simple algorithm for uniform sampling on the surface of a hypersphere

We propose a simple method for uniform sampling of points on the surface of a hypersphere in arbitrarily many dimensions. By avoiding the evaluation of computationally expensive functions like logarithms, sines, cosines, or higher order roots the new method is faster than alternative techniques.

math.NA↗

arXiv2020

Nonflat Histogram Techniques for Spin Glasses

We study the bimodal Edwards-Anderson spin glass comparing established methods, namely the multicanonical method, the $1/k$-ensemble and parallel tempering, to an approach where the ensemble is modified by simulating power-law-shaped histograms in energy instead of flat histograms as in the standard multicanonical case. We show that by this modification a significant speed-up in terms of mean round-trip times can be achieved for all lattice sizes taken into consideration.

cond-mat.dis-nn↗

arXiv2019

Polymer simulation by means of tree data-structures and a parsimonious Metropolis algorithm

We show how a Monte Carlo method for generating self-avoiding walks on lattice geometries which employs a binary-tree data structure can be adapted for hard-sphere polymers with continuous degrees of freedom. Data suggests that the time per Monte Carlo move scales logarithmically with polymer size. We combine the method with a variant of the Metropolis algorithm and preserve this scaling for Lennard-Jones polymers with untruncated monomer-monomer interaction. We further show how the replica-exchange method can be adapted for the same purpose.

cond-mat.stat-mech↗

arXiv2018

Dynamic Greedy Algorithms for the Edwards-Anderson Model

To provide a novel tool for the investigation of the energy landscape of the Edwards-Anderson spin-glass model we introduce an algorithm that allows an efficient execution of a greedy optimization based on data from a previously performed optimization for a similar configuration. As an application we show how the technique can be used to perform higher-order greedy optimizations and simulated annealing searches with improved performance.

cond-mat.dis-nn↗

arXiv2018

Distribution of metastable states of Ising spin glasses

Local minima also known as inherent structures are expected to play an essential role for the behavior of spin glasses. Here, we propose techniques to efficiently sample these configurations in Monte Carlo simulations. For the Sherrington-Kirkpatrick and the three-dimensional Edwards-Anderson model their spectra are determined and compared to analytical results.

cond-mat.dis-nn↗

arXiv2016

Best-case performance of quantum annealers on native spin-glass benchmarks: How chaos can affect success probabilities

Recent tests performed on the D-Wave Two quantum annealer have revealed no clear evidence of speedup over conventional silicon-based technologies. Here, we present results from classical parallel-tempering Monte Carlo simulations combined with isoenergetic cluster moves of the archetypal benchmark problem-an Ising spin glass-on the native chip topology. Using realistic uncorrelated noise models for the D-Wave Two quantum annealer, we study the best-case resilience, i.e., the probability that the ground-state configuration is not affected by random fields and random-bond fluctuations found on the chip. We thus compute classical upper-bound success probabilities for different types of disorder used in the benchmarks and predict that an increase in the number of qubits will require either error correction schemes or a drastic reduction of the intrinsic noise found in these devices. We outline strategies to develop robust, as well as hard benchmarks for quantum annealing devices, as well as any other computing paradigm affected by noise.

quant-ph↗

arXiv2014

Identifying transitions in finite systems by means of partition function zeros and microcanonical inflection-point analysis: A comparison for elastic flexible polymers

For the estimation of transition points of finite elastic, flexible polymers with chain lengths from $13$ to $309$ monomers, we compare systematically transition temperatures obtained by the Fisher partition function zeros approach with recent results from microcanonical inflection-point analysis. These methods rely on accurate numerical estimates of the density of states, which have been obtained by advanced multicanonical Monte Carlo sampling techniques. Both the Fisher zeros method and microcanonical inflection-point analysis yield very similar results and enable the unique identification of transition points in finite systems, which is typically impossible in the conventional canonical analysis of thermodynamic quantities.

physics.data-an↗

arXiv2012

Advanced multicanonical Monte Carlo methods for efficient simulations of nucleation processes of polymers

The investigation of freezing transitions of single polymers is computationally demanding, since surface effects dominate the nucleation process. In recent studies we have systematically shown that the freezing properties of flexible, elastic polymers depend on the precise chain length. Performing multicanonical Monte Carlo simulations, we faced several computational challenges in connection with liquid-solid and solid-solid transitions. For this reason, we developed novel methods and update strategies to overcome the arising problems. We introduce novel Monte Carlo moves and two extensions to the multicanonical method.

cond-mat.soft↗

arXiv2012

Fictitious excitations in the classical Heisenberg antiferromagnet on the kagome lattice

Using an advanced Monte Carlo algorithm and high precision spin dynamics simulation, we investigated the dynamical behavior of the Heisenberg antiferromagnet on a kagome lattice at extremely low temperatures. We demonstrate that the detection and correct identification of propagating excitations depends crucially on the choice of coordinates and we show how modes are displaced in Fourier space if a single, global Cartesian coordinate system is chosen.

cond-mat.str-el↗

arXiv2011

Microcanonical entropy inflection points: Key to systematic understanding of transitions in finite systems

We introduce a systematic classification method for the analogs of phase transitions in finite systems. This completely general analysis, which is applicable to any physical system and extends towards the thermodynamic limit, is based on the microcanonical entropy and its energetic derivative, the inverse caloric temperature. Inflection points of this quantity signal cooperative activity and thus serve as distinct indicators of transitions. We demonstrate the power of this method through application to the long-standing problem of liquid-solid transitions in elastic, flexible homopolymers.

cond-mat.stat-mech↗

arXiv2010

Elastic Lennard-Jones Polymers Meet Clusters -- Differences and Similarities

We investigate solid-solid and solid-liquid transitions of elastic flexible off-lattice polymers with Lennard-Jones monomer-monomer interaction and anharmonic springs by means of sophisticated variants of multicanonical Monte Carlo methods. We find that the low-temperature behavior depends strongly and non-monotonically on the system size and exhibits broad similarities to unbound atomic clusters. Particular emphasis is dedicated to the classification of icosahedral and non-icosahedral low-energy polymer morphologies.

cond-mat.soft↗

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↗

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↗