The phase diagram of two-dimensional continuous particle systems is studied using the event-chain Monte Carlo algorithm. For soft disks with repulsive power-law interactions $\ensuremath{\propto}{r}^{\ensuremath{-}n}$ $n\ensuremath{\gtrsim}6$, recently established hard-disk melting scenario ($n\ensuremath{\rightarrow}\ensuremath{\infty}$) holds: a first-order liquid-hexatic and hexatic-solid transition are identified. Close to $n=6$, coexisting liquid exhibits very long orientational...

Local structure characterization with the bond-orientational order parameters q4, q6, … introduced by Steinhardt et al. [Phys. Rev. B 28, 784 (1983)10.1103/PhysRevB.28.784] has become a standard tool in condensed matter physics, applications including glass, jamming, melting or crystallization transitions, and cluster formation. Here, we discuss two fundamental flaws definition of these that significantly affect their interpretation for studies disordered systems, offer remedy. First,...

Abstract Predicting physical properties of materials with spatially complex structures is one the most challenging problems in material science. One key to a better understanding such geometric characterization their spatial structure. Minkowski tensors are tensorial shape indices that allow quantitative anisotropy and particularly well suited for developing structure‐property relationships tensor‐valued or orientation‐dependent properties. They fundamental indices, some sense being simplest...

In this article, we present an event-driven algorithm that generalizes the recent hard-sphere event-chain Monte Carlo method without introducing discretizations in time or space. A factorization of Metropolis filter and concept infinitesimal moves are used to design a rejection-free Markov-chain for particle systems with arbitrary pairwise interactions. The breaks detailed balance, but satisfies maximal global balance performs better than classic, local large systems. new generates continuum...

Abstract Partitioning space into cells with certain extreme geometrical properties is a central problem in many fields of science and technology. Here we investigate the Quantizer problem, defined as optimisation moment inertia Voronoi cells, i.e., similarly-sized ‘sphere-like’ polyhedra that tile are preferred. We employ Lloyd’s centroidal diagram algorithm to solve this find it converges disordered states associated deep local minima. These universal sense their structure factors...

Quantitative measures for anisotropic characteristics of spatial structure are needed when relating the morphology microstructured heterogeneous materials to tensorial physical properties such as elasticity, permeability and conductance. Tensor-valued Minkowski functionals, defined in framework integral geometry, provide a concise set descriptors morphology. In this article, we describe robust computation these microscopy images polygonal shapes. We demonstrate their relevance shape...

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology anisotropy analysis complex spatial structure using tensor-valued Minkowski functionals, so-called tensors. tensors are generalisations well-known scalar functionals explicitly sensitive anisotropic aspects morphology, relevant example elastic moduli or permeability microstructured materials. Here we derive linear-time compute these tensorial measures three-dimensional shapes....

Several approaches to quantitative local structure characterization for particulate assemblies, such as structural glasses or jammed packings, use the partition of space provided by Voronoi diagram. The conventional construction spherical mono-disperse particles, which cell a particle is that its centre point, cannot be applied configurations aspherical polydisperse particles. Here, we discuss Set diagram particles in three-dimensional space. given composed all points are closer surface (as...

Active matter has been intensely studied for its wealth of intriguing properties such as collective motion, motility-induced phase separation (MIPS), and giant fluctuations away from criticality. However, the precise connection active materials with their equilibrium counterparts remained unclear. For two-dimensional (2D) systems, this is also because experimental theoretical understanding liquid, hexatic, solid phases transitions very recent. Here, we use self-propelled particles...

The quantum-critical properties of the transverse-field Ising model with algebraically decaying interactions are investigated by means stochastic series expansion quantum Monte Carlo, on both one-dimensional linear chain and two-dimensional square lattice. We extract critical exponents $\ensuremath{\nu}$ $\ensuremath{\beta}$ as a function decay exponent long-range interactions. For ferromagnetic interactions, we resolve limiting regimes known from field theory, ranging nearest-neighbor to...

The local structure of disordered jammed packings monodisperse spheres without friction, generated by the Lubachevsky-Stillinger algorithm, is studied for packing fractions above and below $64%$. structural similarity particle environments to fcc or hcp crystalline (local crystallinity) quantified order metrics based on rank-four Minkowski tensors. We find a critical fraction ${\ensuremath{\varphi}}_{\mathrm{c}}\ensuremath{\approx}0.649$, distinctly higher than previously reported values...

In particulate systems with short-range interactions, such as granular matter or simple fluids, local structure plays a pivotal role in determining the macroscopic physical properties. Here, we analyse metrics derived from Voronoi diagram of configurations oblate ellipsoids, for various aspect ratios $\alpha$ and global volume fractions $\phi_g$. We focus on jammed static frictional obtained by tomographic imaging discrete element method simulations. particular, consider packing fraction...

We study the critical breakdown of two-dimensional quantum magnets in presence algebraically decaying long-range interactions by investigating transverse-field Ising model on square and triangular lattice. This is achieved technically combining perturbative continuous unitary transformations with classical Monte Carlo simulations to extract high-order series for one-particle excitations high-field paramagnet. find that unfrustrated systems change from mean-field nearest-neighbor universality...

The hyperscaling relation and standard finite-size scaling (FSS) are known to break down above the upper critical dimension due dangerous irrelevant variables. We establish a coherent formalism for FSS at quantum phase transitions following recently introduced Q-FSS thermal transitions. Contrary long-standing belief, correlation sector is affected by presented recovers generalized form. Using this new formalism, we determine full set of exponents long-range transverse-field Ising chain in...

We investigate the emergence of subdiffusive transport by obstruction in continuum models for molecular crowding. While underlying percolation transition accessible space displays universal behavior, dynamic properties depend a subtle nonuniversal way on through narrow channels. At same time, different universality classes are robust with respect to introducing correlations obstacle matrix as we demonstrate quenched hard-sphere liquids structures. Our results confirm that microscopic...

We study the continuous one-dimensional hard-sphere model and present irreversible local Markov chains that mix on faster time scales than reversible heat bath or Metropolis algorithms. The mixing appear to fall into two distinct universality classes, both for chains. event-chain algorithm, infinitesimal limit of one these chains, belongs class presenting fastest decay. For lattice-gas model, correspond symmetric simple exclusion process (SEP) with periodic boundary conditions. classes are...

Abstract The effective linear‐elastic moduli of disordered network solids are analyzed by voxel‐based finite element calculations. We analyze given Poisson‐Voronoi processes and the structure collagen fiber networks imaged confocal microscopy. solid volume fraction ϕ is varied adjusting radius, while keeping structural mesh or pore size underlying fixed. For intermediate , bulk shear modulus approximated empirical power‐laws $ K(\phi) \propto \phi^n$ G(\phi) \phi^m$ with n ≈ 1.4 m 1.7....

Inverse bicontinuous cubic phases with two aqueous network domains separated by a smooth bilayer are firmly established as equilibrium in lipid/water systems. The purpose of this article is to highlight the generalisations these geometries polycontinuous geometries, which could be realised lipid mesophases three or more network-like branched bilayer. An analysis structural homogeneity terms width variations reveals that ordered likely candidates for mesophase structures, similar chain...

To gain a better understanding of the interplay between frustrated long-range interactions and zero-temperature quantum fluctuations, we investigate ground-state phase diagram transverse-field Ising model with algebraically decaying on quasi-one-dimensional infinite-cylinder triangular lattices. Technically, apply various approaches including low- high-field series expansions. For classical model, cylinders an arbitrary even circumference. We show occurrence gapped stripe-ordered phases...

We present a rigorous efficient event-chain Monte Carlo algorithm for long-range interacting particle systems. Using cell-veto scheme within the factorized Metropolis algorithm, we compute each single-particle move with fixed number of operations. For slowly decaying potentials such as Coulomb interactions, screening line charges allow us to take into account periodic boundary conditions. discuss performance general inverse-power-law potentials, and illustrate how it provides new outlook on...

Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, structural glasses. Minkowski tensors provide a set shape measures that are based on strong mathematical theorems easily computed polygonal polyhedral bodies such as cells (Voronoi cells). They characterize local structure beyond two-point correlation function suitable define indices 0 ≤ βνa, b 1 anisotropy. Here, we analyze statistics...

The hard-disk problem, the statics and dynamics of equal two-dimensional hard spheres in a periodic box, has had profound influence on statistical computational physics. Markov-chain Monte Carlo molecular were first discussed for this model. Here we reformulate algorithms terms another classic namely sampling from polytope. Local Carlo, as proposed by Metropolis et al. 1953, appears sequence random walks high-dimensional polytopes, while moves more powerful event-chain algorithm correspond...

We explore the growth of two-dimensional quasicrystals, i.e., aperiodic structures that possess long-range order, from two seeds at various distances and with different orientations by using dynamical phase-field crystal calculations. compare results to periodic crystals seeds. There, a domain border consisting dislocations is observed in case large between seed angles their orientation. Furthermore, found if are placed distance does not fit lattice. In we only observe borders for...

We report that a specific realization of Schwarz's triply periodic hexagonal minimal surface is isotropic with respect to the Doi-Ohta interface tensor and simultaneously has packing stretching frustration similar those commonly found cubic bicontinuous mesophases. This surface, symmetry P6(3)/mmc lattice ratio c/a = 0.832, therefore likely candidate geometry for self-assembled lipid/surfactant or copolymer Furthermore, both peak position ratios in its powder diffraction pattern elastic...