arXiv subjects

Wolfhard Janke

Publications and source records attributed to Wolfhard Janke.

At least 19 recordsLinked to original sources

arXiv2026

Meandering stripes in the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice

We study the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice with ferromagnetic nearest-neighbor couplings fixed at $J_1=1$ and strong antiferromagnetic next-nearest-neighbor interactions, i.e., $J_2 \leq -1/4$. Little is known for this range of $J_2$, whereas for less negative values of $J_2$ the system orders ferromagnetically at low temperatures and appears to remain in the Ising universality class. In previous work it was shown that the model has a largely degenerate ground state, and it was conjectured that there is some kind of phase transition. We introduce a complex-valued nematic order parameter, which can differentiate between the high-temperature paramagnetic phase and the observed partially-disordered stripe phase at lower temperatures. Configurations in this phase consist of stripes of spins parallel with respect to one lattice direction, which collectively meander along the remaining two, producing partially disordered ground states. The sharp peaks in the specific heat observed in earlier work only appear when using periodic boundary conditions and are absent for free boundaries. Additionally, we reveal a striking dependence of the behavior on the aspect ratio of the considered samples. Ultimately, even a careful finite-size scaling analysis for $J_2 = -0.5$ and $J_2 = -1$ is unable to clearly discern between a crossover without any singularities and some form of continuous transition, including the possibility of an infinite-order transition of the Berezinskii-Kosterlitz-Thouless (BKT) type. For $J_2=-1/4$ we find that the system remains disordered at all temperatures and that it exhibits a finite ground-state entropy per site, for which our simulations provide the accurate asymptotic estimate $S(T=0)/N = 0.230\,960\,93(14)$ in the thermodynamic limit $N\rightarrow\infty$.

cond-mat.stat-mech↗

arXiv2026

Harnessing finite-size effects to gauge aging in the $2D$ Ising model

The relaxation behavior towards equilibrium of the $2D$ Ising model with nearest-neighbor interactions has been studied with focus on the two-time autocorrelator $C(t,s)$. Finite-size effects affecting the growing magnetic domains lead to the saturation of $C(t,s)$ with a distinct plateau of height $C_{\infty}^{(2)}(s,L)$ scaling algebraically with waiting time $s$ and lattice size $L$. These scaling relations are used to produce precise estimates for the autocorrelation exponent $\lambda$ and dynamical exponent $z$ with deliberately small lattices. Treating smooth domain walls in a similar manner to the lattice boundaries, their effect on $C(t,s)$ can be understood as premature finite-size phenomenon, extending our ansatz to systems not yet in equilibrium.

cond-mat.stat-mech↗

arXiv2025

Frustrated Ising model on the honeycomb lattice: Metastability and universality

We study the Ising model with competing ferromagnetic nearest- and antiferromagnetic next-nearest-neighbor interactions of strengths $J_1 > 0$ and $J_2 < 0$, respectively, on the honeycomb lattice. For $J_2 > - J_1 / 4$ it has a ferromagnetic ground state, and previous work has shown that at least for $J_2 \gtrsim -0.2 J_1$ the transition is in the Ising universality class. For even lower $J_2$ some indicators pointing towards a first-order transition were reported. By utilizing population annealing Monte Carlo simulations together with a rejection-free and adaptive update, we can equilibrate systems with $J_2$ as low as $-0.23 J_1$. By means of a finite-size scaling analysis we show that the system undergoes a second-order phase transition within the Ising universality class at least down to $J_2 =-0.23 J_1$ and, most likely, for all $J_2 > - J_1 / 4$. As we show here, there exist very long-lived metastable states in this system explaining the first-order like behavior seen in only partially equilibrated systems.

cond-mat.stat-mech↗

arXiv2025

Influence of Thermostats on the Dynamics of the Helix-Coil Transition

We present results from all-atom molecular dynamics simulations for the nonequilibrium dynamics of the collapse and helix-coil transition in polyalanine. In particular, we compare the influence of three different thermostats, viz., the Langevin, Andersen, and Nos\'e-Hoover thermostats. For that purpose, we investigate the nonequilibrium pathways of the transition from the high-temperature random-coil state to the low-temperature helical state. Additionally, we analyze the time evolution of the potential energy and temperature. Our results show only small differences in the observed phenomenology, albeit quantitatively the dynamics appear to be different for the three thermostats.

cond-mat.soft↗

arXiv2025

Nonequilibrium Dynamics of the Helix-Coil Transition in Polyalanine

In this work, the nonequilibrium pathways of the collapse of the helix-forming biopolymer polyalanine are investigated. To this end, the full time evolution of the helix-coil transition is simulated using molecular dynamics simulations. At the start of the transition short $3_{10}$-helices form, seemingly leading to the molecule becoming more aspherical midway through the collapse. After the completed collapse, the formation of $\alpha$-helices seems to become the prevalent ordering mechanism leading to helical bundles, a structure representative for the equilibrium behavior of longer chains. The dynamics of this transition is explored in terms of the power-law scaling of two associated relaxation times as a function of the chain length.

cond-mat.soft↗

arXiv2025

Efficient predecision scheme for Metropolis Monte Carlo simulation of long-range interacting lattice systems

We propose a fast and general predecision scheme for Metropolis Monte Carlo simulation of $d$-dimensional long-range interacting lattice models. For potentials of the form $V(r)=r^{-d-\sigma}$, this reduces the computational complexity from $O\left(N^2\right)$ to $O\left(N^{2-\sigma/d}\right)$ for $\sigma < d$ and to $O\left(N \right)$ for $\sigma > d$, respectively. The algorithm is implemented and tested for several $\mathrm{O}(n)$ spin models ranging from the Ising over the XY to the Edwards-Anderson spin-glass model. With the same random number sequence it produces exactly the same Markov chain as a simulation with explicit summation of all terms in the Hamiltonian. Due to its generality, its simplicity, and its reduced computational complexity it has the potential to find broad application and thus lead to a deeper understanding of the role of long-range interactions in the physics of lattice models, especially in nonequilibrium settings.

cond-mat.stat-mech↗

arXiv2025

Finite-Size Effects in Aging can be Interpreted as Sub-Aging

Systems brought out of equilibrium through a rapid quench from a disordered initial state into an ordered phase undergo physical aging in the form of phase-ordering kinetics, with characteristic dynamical scaling. In many systems, notably glasses, dynamical scaling is often described through sub-aging, where a phenomenological sub-aging exponent $0<\mu< 1$ is empirically chosen to achieve the best possible data collapse. Here it is shown that finite-size effects modify the dynamical scaling behavior, away from simple aging with $\mu=1$ towards $\mu<1$, such that phenomenologically it would appear as sub-aging. This is exemplified for the exactly solved dynamical spherical model in dimensions $2<d<4$ and numerical simulations of the two-dimensional Ising model, with short-ranged and long-ranged interactions.

cond-mat.stat-mech↗

arXiv2024

Partition function zeros of the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice

We study the zeros of the partition function in the complex temperature plane (Fisher zeros) and in the complex external field plane (Lee-Yang zeros) of a frustrated Ising model with competing nearest-neighbor ($J_1 > 0$) and next-nearest-neighbor ($J_2 < 0$) interactions on the honeycomb lattice. We consider the finite-size scaling (FSS) of the leading Fisher and Lee-Yang zeros as determined from a cumulant method and compare it to a traditional scaling analysis based on the logarithmic derivative of the magnetization $\partial \ln \langle |M| \rangle /\partial\beta$ and the magnetic susceptibility $\chi$. While for this model both FSS approaches are subject to strong corrections to scaling induced by the frustration, their behavior is rather different, in particular as the ratio $\mathcal{R} = J_2/J_1$ is varied. As a consequence, an analysis of the scaling of partition function zeros turns out to be a useful complement to a more traditional FSS analysis. For the cumulant method, we also study the convergence as a function of cumulant order, providing suggestions for practical implementations. The scaling of the zeros convincingly shows that the system remains in the Ising universality class for $\mathcal{R}$ as low as $-0.22$, where results from traditional FSS using the same simulation data are less conclusive. The approach hence provides a valuable additional tool for mapping out the phase diagram of models afflicted by strong corrections to scaling.

cond-mat.stat-mech↗

arXiv2024

Non-universality of aging during phase separation of the two-dimensional long-range Ising model

We investigate the aging properties of phase-separation kinetics following quenches from $T=\infty$ to a finite temperature below $T_c$ of the paradigmatic two-dimensional conserved Ising model with power-law decaying long-range interactions $\sim r^{-(2 + \sigma)}$. Physical aging with a power-law decay of the two-time autocorrelation function $C(t,t_w)\sim \left(t/t_w\right)^{-\lambda/z}$ is observed, displaying a complex dependence of the autocorrelation exponent $\lambda$ on $\sigma$. A value of $\lambda=3.500(26)$ for the corresponding nearest-neighbor model (which is recovered as the $\sigma \rightarrow \infty$ limes) is determined. The values of $\lambda$ in the long-range regime ($\sigma < 1$) are all compatible with $\lambda \approx 4$. In between, a continuous crossover is visible for $1 \lesssim \sigma \lesssim 2$ with non-universal, $\sigma$-dependent values of $\lambda$. The performed Metropolis Monte Carlo simulations are primarily enabled by our novel algorithm for long-range interacting systems.

cond-mat.stat-mech↗

arXiv2024

Temperature and Solvent Viscosity Tune the Intermediates During the Collapse of a Polymer

Dynamics of a polymer chain in solution gets significantly affected by the temperature and the frictional forces arising due to solvent viscosity. Here, using an explicit solvent framework for polymer simulation with the liberty to tune the solvent viscosity, we study the nonequilibrium dynamics of a flexible homopolymer when it is suddenly quenched from an extended coil state in good solvent to poor solvent conditions. Results from our extensive simulations reveal that depending on the temperature $T$ and solvent viscosity, one encounters long-lived sausage-like intermediates following the usual pearl-necklace intermediates. Use of shape factors of polymers allows us to disentangle these two distinct stages of the overall collapse process, and the corresponding relaxation times. The relaxation time $τ_s$ of the sausage stage, which is the rate-limiting stage of the overall collapse process, follows an anti-Arrhenius behavior in the high-$T$ limit, and the Arrhenius behavior in the low-$T$ limit. Furthermore, the variation of $τ_s$ with the solvent viscosity provides evidence of internal friction of the polymer, that modulates the overall collapse significantly, analogous to what is observed for relaxation rates of proteins during their folding. This suggests that the origin of internal friction in proteins is plausibly intrinsic to its polymeric backbone rather than other specifications.

cond-mat.soft↗

arXiv2024

Aging following a zero-temperature quench in the $d=3$ Ising model

Aging in phase-ordering kinetics of the $d=3$ Ising model following a quench from infinite to zero temperature is studied by means of Monte Carlo simulations. In this model the two-time spin-spin autocorrelator $C_\text{ag}$ is expected to obey dynamical scaling and to follow asymptotically a power-law decay with the autocorrelation exponent $\lambda$. Previous work indicated that the lower Fisher-Huse bound of $\lambda\geq d/2 = 1.5$ is violated in this model. Using much larger systems than previously studied, the instantaneous exponent for $\lambda$ we obtain at late times does \emph{not} disagree with this bound. By conducting systematic fits to the data of $C_\text{ag}$ using different ansaetze for the leading correction term, we find $\lambda = 1.58(14)$ with most of error attributed to the systematic uncertainty regarding the ansaetze. This result is in contrast to the recent report that below the roughening transition universality might be violated.

cond-mat.stat-mech↗

arXiv2024

Thermodynamically Stable Knots in Semiflexible Polymers

Semiflexible polymers are widely used as a paradigm for understanding structural phases in biomolecules including folding of proteins. Here, we compare bead-spring and bead-stick variants of coarse-grained semiflexible polymer models that cover the whole range from flexible to stiff by conducting extensive replica-exchange Monte Carlo computer simulations. In the data analysis we focus on knotted conformations whose stability is shown to depend on the ratio $r_b/r_{\rm min}$ with $r_b$ denoting the equilibrium bond length and $r_{\rm min}$ the distance of the strongest nonbonded interactions. For both models, our results provide evidence that at low temperatures for $r_b/r_{\rm min}$ outside a small range around unity one always encounters knots as generic stable phases along with the usual frozen and bent-like structures. By varying the bending stiffness, we observe rather strong first-order-like structural transitions between the coexisting phases characterized by these geometrically different motifs. Through analyses of the energy distributions close to the transition point, we present exploratory estimates of the free-energy barriers between the coexisting phases.

cond-mat.soft↗

arXiv2024

Spontaneous Micro Flocking of Active Inertial Particles without Alignment Interaction

Observing spontaneous velocity ordering or flocking during motility induced phase separation (MIPS) in a system of spherical active Brownian particles without alignment interaction is challenging. We take up this problem by performing simulations of spherical active inertial particles with purely repulsive potential in presence of thermal noise and absence of any explicit alignment interaction. Our results not only show the presence of MIPS, but also reveal a micro-flocking transition. We characterize this transition in terms of a velocity order parameter as well as a characteristic length scale derived from the spatial correlation of the velocities.

cond-mat.soft↗

arXiv2024

Resampling schemes in population annealing: Numerical and theoretical results

The population annealing algorithm is a population-based equilibrium version of simulated annealing. It can sample thermodynamic systems with rough free-energy landscapes more efficiently than standard Markov chain Monte Carlo alone. A number of parameters can be fine-tuned to improve the performance of the population annealing algorithm. While there is some numerical and theoretical work on most of these parameters, there appears to be a gap in the literature concerning the role of resampling in population annealing which this work attempts to close. The two-dimensional Ising model is used as a benchmarking system for this study. At first various resampling methods are implemented and numerically compared. In a second part the exact solution of the Ising model is utilized to create an artificial population annealing setting with effectively infinite Monte Carlo updates at each temperature. This limit is first performed on finite population sizes and subsequently extended to infinite populations. This allows us to look at resampling isolated from other parameters. Many results are expected to generalize to other systems.

cond-mat.stat-mech↗

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

Activity Induced Enhanced Diffusion of a Polymer in Poor Solvent

By means of Brownian dynamics simulations we study the steady-state dynamic properties of a flexible active polymer in a poor solvent condition. Our results show that the effective diffusion constant of the polymer $D_{\rm eff}$ gets significantly enhanced as activity increases, much like in active particles. The simulation data are in agreement with a theoretically constructed Rouse model of active polymer, demonstrating that irrespective of the strength of activity, the long-time dynamics of the polymer chain is characterized by a universal Rouse-like scaling $D_{\rm eff} \sim N^{-1}$, where $N$ is the chain length.

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

Superdiffusion-like behavior in zero-temperature coarsening of the $d=3$ Ising model

One key aspect of coarsening following a quench below the critical temperature is domain growth. For the non-conserved Ising model a power-law growth of domains of like spins with exponent $α= 1/2$ is predicted. Including recent work, it was not possible to clearly observe this growth law in the special case of a zero-temperature quench in the three-dimensional model. Instead a slower growth with $α<1/2$ was reported. We attempt to clarify this discrepancy by running large-scale Monte Carlo simulations of lattice sizes up to $L=2048$ employing an efficient GPU implementation. Indeed, at late times we measure domain sizes compatible with the expected growth law -- but surprisingly, at still later times domains even grow superdiffusively, i.e., with $α> 1/2$. We argue that this new problem is possibly caused by sponge-like structures emerging at early times.

cond-mat.stat-mech↗