arXiv subjects

Martin Weigel

Publications and source records attributed to Martin Weigel.

At least 19 recordsLinked to original sources

arXiv2026

Accurate ground-state entropies from population Monte Carlo: The antiferromagnetic Ising model on the Shastry-Sutherland lattice

We demonstrate how the population annealing Monte Carlo simulation method can be used to compute the ground-state entropy to high precision. This approach is tested for the classical antiferromagnetic Ising model on the Shastry-Sutherland lattice with diagonal couplings chosen twice as strong as the nearest-neighbor interactions. In the absence of an external magnetic field, the model is known to be disordered at all temperatures, with a macroscopically degenerate ground state. We find the ground-state entropy to be $0.458\,777\,78(10)$ per site, which is in good agreement with the estimate of a recent study using the corner transfer matrix renormalization group method. The sampled ground-state configurations are analyzed by considering the bond configurations, the local-energy configurations, and the spin-spin correlations. While all observations are consistent with the disordered nature of the ground state, the numerical data suggest a power-law decay of the size distribution of clusters of sites with local energies different from the ground-state level.

cond-mat.stat-mech↗

arXiv2026

Anomalous Behavior in Systems with Delay

In a recent letter [Phys. Rev. E 112, L042201 (2025)], we demonstrated the occurrence of anomalous diffusion, weak chaos, and weak ergodicity breaking in a certain class of time-delayed feedback systems with linear instantaneous and nonlinear delayed term. This anomalous behavior is caused by the trapping of chaotic solutions close to nonhyperbolic fixed-point solutions in function space. In this paper, we extend our previous study, present more detailed insights, and show surprising new results. We first investigate the case of a constant delay, where the dynamical behavior during such trapping events can be explained by center manifold theory. In the large-delay limit, the probability for the trapping events becomes small because of a high effective dimension of the chaotic phases. As a consequence, anomalous behavior is only observable on very large time scales. By introducing a periodic modulation of the delay time, trapping events become more probable with increasing modulation amplitude due to a reduction of the effective dimension and the occurrence of laminar chaos. For large values of the modulation amplitude, the anomalous behavior is more complex and the most relevant aspects can be reproduced by a two-dimensional iterated map and a stochastic model.

nlin.CD↗

arXiv2026

Glassiness and dynamic arrest in magnetic and non-magnetic colloids

We investigate and compare a range of indicators for glassiness in monodisperse magnetic and non-magnetic soft-sphere fluids at low temperatures with a view to exploring the effect of the magnetic moment. We perform extensive molecular dynamics simulations using the Stockmayer model for magnetic fluids and a pure Lennard-Jones interaction for the non-magnetic case. Our investigations involve quenching experiments, in which both systems are rapidly cooled deep below their freezing temperatures. Although the Lennard-Jones fluid forms compact aggregates, the inclusion of dipolar interactions promotes the development of branched and open morphologies. After characterizing the static properties of the frozen structures, we focus on their dynamics. A key observable is the self-part of the van Hove function, which measures the probability that a particle is displaced by a distance $Δ$ over time $t$. In both fluids, this function exhibits non-Gaussian behavior --- thereby providing a signature of dynamic heterogeneity and glassiness. This behavior stems from a separation of time scales between two distinct processes: mobile particles that escape their environments and immobile particles that vibrate within cages. In particular, we find a heavier tail in the van Hove function for the Stockmayer fluid, which is a consequence of the strongly correlated motion in chain-like structures found there. These findings shed light on core relaxation mechanisms in magnetic fluids, advancing our understanding of magnetically responsive colloidal systems.

cond-mat.soft↗

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

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↗

arXiv2026

Cluster percolation and dynamical scaling in the Baxter--Wu model

We investigate the percolation behavior of Fortuin-Kasteleyn--type clusters in the spin-$1/2$ Baxter--Wu model with three-spin interactions on a triangular lattice. The considered clusters are constructed by randomly freezing one of the three sublattices, resulting in effective pairwise interactions among the remaining spins. Using Monte Carlo simulations combined with a finite-size scaling analysis, we determine the percolation temperature of these stochastic clusters and show that it coincides with the exact thermal critical point of the model. The critical exponents derived from cluster observables are consistent with those of the underlying thermal phase transition. Finally, we analyze the dynamical scaling of the multi-cluster and single-cluster algorithms resulting from the cluster construction, highlighting their efficiency and scaling behavior with system size.

cond-mat.stat-mech↗

arXiv2025

The Physics of Local Optimization in Complex Disordered Systems

Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e., the complexity of predicting local properties of the solution from local information, for the ground-state problem of both P- and NP-hard spin-glasses and related frustrated spin systems. Depending on the model considered, we observe varying scaling behaviors in how errors associated with local predictions decay as a function of the size of the solved subsystem. These errors are intimately connected to global critical threshold instabilities, characterized by gapless, avalanche-like excitations that follow scale-invariant size distributions. Away from criticality, local solvers quickly achieve high accuracy, aligning closely with the results of the computationally much more expensive global minimization. We leverage these findings to introduce a heuristic contraction-based algorithm for globally studying spin-glass ground states. The local solvers further display sharp imprints of the phase transition from the spin-glass to the ferromagnetic phase as the distribution of spin-glass couplings is shifted, as well as characteristic differences for the infinite-range model, implying the existence of specific classes of local hardness. Our findings shed light on how Nature may operate solely through local actions at her disposal.

cond-mat.dis-nn↗

arXiv2025

Cluster percolation in the three-dimensional $\pm J$ random-bond Ising model

Based on extensive parallel-tempering Monte Carlo simulations, we investigate the relationship between cluster percolation and equilibrium ordering phenomena in the three-dimensional $\pm J$ random-bond Ising model as one varies the fraction of antiferromagnetic bonds. We consider a range of cluster definitions, most of which are constructed in the space of overlaps between two independent real replicas of the system. In the pure ferromagnet that is contained as a limiting case in the class of problems considered, the relevant percolation point coincides with the thermodynamic ordering transition. For the disordered ferromagnet encountered first on introducing antiferromagnetic bonds and the adjacent spin-glass phase of strong disorder this connection is altered, and one finds a percolation transition above the thermodynamic ordering point that is accompanied by the appearance of /two/ percolating clusters of equal density. Only at the lower (disordered) ferromagnetic or spin-glass transition points the densities of these two clusters start to diverge, thus providing a percolation signature of these thermodynamic transitions. We compare the scaling behavior at this secondary percolation transition with the thermodynamic behavior at the corresponding ferromagnetic and spin-glass phase transitions.

cond-mat.dis-nn↗

arXiv2025

Ordering transition of the three-dimensional four-state random-field Potts model

Spin systems exposed to the influence of random magnetic fields are paradigmatic examples for studying the effect of quenched disorder on condensed-matter systems. In this context, previous studies have almost exclusively focused on systems with Ising or continuous symmetries, while the Potts symmetry, albeit being of fundamental importance also for the description of realistic physical systems, has received very little attention. In the present study, we use a recently developed quasi-exact method for determining ground states in the random-field Potts model to study the problem with four states. Extending the protocol applied for the three-state model, we use extensive finite-size scaling analyses of the magnetization, Binder parameter, energy cumulant, specific heat, and the connected as well as disconnected susceptibilities to study the magnetic ordering transition of the model. In contrast to the system in the absence of disorder, we find compelling evidence for a continuous transition, and we precisely determine the critical point as well as the critical exponents, which are found to differ from the exponents of the three-state system as well as from those of the random-field Ising model.

cond-mat.stat-mech↗

arXiv2024

The Griffiths phase and beyond: A large deviations study of the magnetic susceptibility of the two-dimensional bond-diluted Ising model

The Griffiths phase in systems with quenched disorder occurs below the ordering transition of the pure system down to the ordering transition of the actual disordered system. While it does not exhibit long-range order, large fluctuations in the disorder degrees of freedom result in exponentially rare, long-range ordered states and hence the occurrence of broad distributions in response functions. Inside the Griffiths phase of the two-dimensional bond-diluted Ising model the distribution of the magnetic susceptibility is expected to have such a broad, exponential tail. A large-deviations Monte Carlo algorithm is used to sample this distribution and the exponential tail is extracted over a wide range of the support down to very small probabilities of the order of $10^{-300}$. We study the behavior of the susceptibility distribution across the full phase diagram, from the paramagnetic state through the Griffiths phase to the ferromagnetically ordered system and down to the zero-temperature point. We extract the rate function of large-deviation theory as well as its finite-size scaling behavior and we reveal interesting differences and similarities between the cases. A connection between the fraction of ferromagnetic bonds in a given disorder sample and the size of the magnetic susceptibility is demonstrated numerically.

cond-mat.dis-nn↗

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 $\partial \ln \langle |M| \rangle /\partialβ$ and the magnetic susceptibility $χ$. 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

Spin glasses and percolation

The description of thermodynamic phase transitions in terms of percolation transitions of suitably defined clusters has a long tradition and boasts a number of important successes, the most prominent ones being in ferromagnetic lattice models. Spin glasses and other frustrated systems are not among them as the clusters of aligned spins usually considered in this context start to percolate in the disordered phase and hence fail to indicate the onset of ordering. In this mini-review we provide an overview of the state of the art in this field, including recent advances, and outline the main open questions in the area.

cond-mat.dis-nn↗

arXiv2024

Universal fragility of spin-glass ground-states under single bond changes

We consider the effect of perturbing a single bond on ground-states of nearest-neighbor Ising spin-glasses, with a Gaussian distribution of the coupling constants, across various two and three-dimensional lattices and regular random graphs. Our results reveal that the ground-states are strikingly susceptible to such changes. Altering the strength of only a single bond beyond a critical threshold value leads to a new ground-state that differs from the original one by a droplet of flipped spins whose boundary and volume diverge with the system size -- an effect that is reminiscent of the more familiar phenomenon of disorder chaos. These elementary fractal-boundary zero-energy droplets and their composites feature robust characteristics and provide the lowest-energy macroscopic spin-glass excitations. Remarkably, within numerical accuracy, the size of such droplets conforms to a nearly universal power-law distribution with exponents dependent on the spatial dimension of the system. Furthermore, the critical coupling strengths adhere to a stretched Gaussian distribution that is predominantly determined by the local coordination number.

cond-mat.dis-nn↗

arXiv2024

Geometric clusters in the overlap of the Ising model

We study the percolation properties of geometrical clusters defined in the overlap space of two statistically independent replicas of a square-lattice Ising model that are simulated at the same temperature. In particular, we consider two distinct types of clusters in the overlap, which we dub soft- and hard-constraint clusters, and which are subsets of the regions of constant spin overlap. By means of Monte Carlo simulations and a finite-size scaling analysis we estimate the transition temperature as well as the set of critical exponents characterizing the percolation transitions undergone by these two cluster types. The results suggest that both soft- and hard-constraint clusters percolate at the critical temperature of the Ising model and their critical behavior is governed by the correlation-length exponent $ν= 1$ found by Onsager. At the same time, they exhibit non-standard and distinct sets of exponents for the average cluster size and percolation strength.

cond-mat.stat-mech↗

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

How contact patterns destabilize and modulate epidemic outbreaks

The spread of a contagious disease clearly depends on when infected individuals come into contact with susceptible ones. Such effects, however, have remained largely unexplored in the study of epidemic outbreaks. In particular, it remains unclear how the timing of contacts interacts with the latent and infectious stages of the disease. Here, we use real-world physical proximity data to study this interaction and find that the temporal statistics of actual human contact patterns i) destabilize epidemic outbreaks and ii) modulate the basic reproduction number. We explain both observations by distinct aspects of the observed contact patterns. On the one hand, we find the destabilization of outbreaks to be caused by temporal clustering of contacts leading to over-dispersed offspring distributions and increased probabilities of otherwise rare events (zero- and super-spreading). Notably, our analysis enables us to disentangle previously elusive sources of over-dispersion in empirical offspring distributions. On the other hand, we find the modulation of R0 to be caused by a periodically varying contact rate. Both mechanisms are a direct consequence of the memory in contact behavior, and we showcase a generative process that reproduces these non-Markovian statistics. Our results point to the importance of including non-Markovian contact timings into studies of epidemic outbreaks.

physics.soc-ph↗

arXiv2023

Cluster Percolation in the Two-Dimensional Ising Spin Glass

Suitable cluster definitions have allowed researchers to describe many ordering transitions in spin systems as geometric phenomena related to percolation. For spin glasses and some other systems with quenched disorder, however, such a connection has not been fully established, and the numerical evidence remains incomplete. Here we use Monte Carlo simulations to study the percolation properties of several classes of clusters occurring in the Edwards-Anderson Ising spin-glass model in two dimensions. The Fortuin-Kasteleyn-Coniglio-Klein clusters originally defined for the ferromagnetic problem do percolate at a temperature that remains non-zero in the thermodynamic limit. On the Nishimori line, this location is accurately predicted by an argument due to Yamaguchi. More relevant for the spin-glass transition are clusters defined on the basis of the overlap of several replicas. We show that various such cluster types have percolation thresholds that shift to lower temperature by increasing the system size, in agreement with the zero-temperature spin-glass transition in two dimensions. The overlap is linked to the difference in density of the two largest clusters, thus supporting a picture where the spin-glass transition corresponds to an emergent density difference of the two largest clusters inside the percolating phase.

cond-mat.dis-nn↗

arXiv2023

Understanding Stationary and Moving Direct Skin Vibrotactile Stimulation on the Palm

Palm-based tactile displays have the potential to evolve from single motor interfaces (e.g., smartphones) to high-resolution tactile displays (e.g., back-of-device haptic interfaces) enabling richer multi-modal experiences with more information. However, we lack a systematic understanding of vibrotactile perception on the palm and the influence of various factors on the core design decisions of tactile displays (number of actuators, resolution, and intensity). In a first experiment (N=16), we investigated the effect of these factors on the users' ability to localize stationary sensations. In a second experiment (N=20), we explored the influence of resolution on recognition rate for moving tactile sensations.Findings show that for stationary sensations a 9 actuator display offers a good trade-off and a $3\times3$ resolution can be accurately localized. For moving sensations, a $2\times4$ resolution led to the highest recognition accuracy, while $5\times10$ enables higher resolution output with a reasonable accuracy.

cs.HC↗