arXiv subjects

Lambert Münster

Publications and source records attributed to Lambert Münster.

5 recordsLinked to original sources

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↗

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↗

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

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↗

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↗