Search results for " Statistical"
showing 10 items of 1649 documents
Unraveling the nature of universal dynamics in $O(N)$ theories
2020
Many-body quantum systems far from equilibrium can exhibit universal scaling dynamics which defy standard classification schemes. Here, we disentangle the dominant excitations in the universal dynamics of highly-occupied $N$-component scalar systems using unequal-time correlators. While previous equal-time studies have conjectured the infrared properties to be universal for all $N$, we clearly identify for the first time two fundamentally different phenomena relevant at different $N$. We find all $N\geq3$ to be indeed dominated by the same Lorentzian ``large-$N$'' peak, whereas $N=1$ is characterized instead by a non-Lorentzian peak with different properties, and for $N=2$ we see a mixture …
Surface tension and interfacial fluctuations in d-dimensional Ising model
2005
The surface tension of rough interfaces between coexisting phases in 2D and 3D Ising models are discussed in view of the known results and some original calculations presented in this paper. The results are summarised in a formula, which allows to interpolate the corrections to finite-size scaling between two and three dimensions. The physical meaning of an analytic continuation to noninteger values of the spatial dimensionality d is discussed. Lattices and interfaces with properly defined fractal dimensions should fulfil certain requirements to possibly have properties of an analytic continuation from d-dimensional hypercubes. Here 2 appears as the marginal value of d below which the (d-1)…
Regular packings on periodic lattices.
2011
We investigate the problem of packing identical hard objects on regular lattices in d dimensions. Restricting configuration space to parallel alignment of the objects, we study the densest packing at a given aspect ratio X. For rectangles and ellipses on the square lattice as well as for biaxial ellipsoids on a simple cubic lattice, we calculate the maximum packing fraction \phi_d(X). It is proved to be continuous with an infinite number of singular points X^{\rm min}_\nu, X^{\rm max}_\nu, \nu=0, \pm 1, \pm 2,... In two dimensions, all maxima have the same height, whereas there is a unique global maximum for the case of ellipsoids. The form of \phi_d(X) is discussed in the context of geomet…
From scalar to polar active matter: Connecting simulations with mean-field theory
2019
We study numerically the phase behavior of self-propelled elliptical particles interacting through the ``hard'' repulsive Gay-Berne potential at infinite P\'eclet number. Changing a single parameter, the aspect ratio, allows us to continuously go from discoid active Brownian particles to elongated polar rods. Discoids show phase separation, which changes to a cluster state of polar domains, which then form polar bands as the aspect ratio is increased. From the simulations, we identify and extract the two effective parameters entering the mean-field description: the force imbalance coefficient and the effective coupling to the local polarization. These two coefficients are sufficient to obta…
Observation of a tricritical wedge filling transition in the 3D Ising model
2014
In this Letter we present evidences of the occurrence of a tricritical filling transition for an Ising model in a linear wedge. We perform Monte Carlo simulations in a double wedge where antisymmetric fields act at the top and bottom wedges, decorated with specific field acting only along the wegde axes. A finite-size scaling analysis of these simulations shows a novel critical phenomenon, which is distinct from the critical filling. We adapt to tricritical filling the phenomenological theory which successfully was applied to the finite-size analysis of the critical filling in this geometry, observing good agreement between the simulations and the theoretical predictions for tricritical fil…
How Does the Relaxation of a Supercooled Liquid Depend on Its Microscopic Dynamics?
1998
Using molecular dynamics computer simulations we investigate how the relaxation dynamics of a simple supercooled liquid with Newtonian dynamics differs from the one with a stochastic dynamics. We find that, apart from the early beta-relaxation regime, the two dynamics give rise to the same relaxation behavior. The increase of the relaxation times of the system upon cooling, the details of the alpha-relaxation, as well as the wave vector dependence of the Edwards-Anderson-parameters are independent of the microscopic dynamics.
The structural relaxation of molten sodium disilicate
2002
We use molecular dynamics computer simulations to study the relaxation dynamics of Na2O-2(SiO2) in its molten, highly viscous state. We find that at low temperatures the incoherent intermediate scattering function for Na relaxes about 100 times faster than the one of the Si and O atoms. In contrast to this all coherent functions relax on the same time scale if the wave-vector is around 1AA^-1. This anomalous relaxation dynamics is traced back to the channel-like structure for the Na atoms that have been found for this system. We find that the relaxation dynamics for Si and O as well as the time dependence of the coherent functions for Na can be rationalized well by means of mode-coupling th…
Microscopic theory of glassy dynamics and glass transition for molecular crystals.
2004
We derive a microscopic equation of motion for the dynamical orientational correlators of molecular crystals. Our approach is based upon mode coupling theory. Compared to liquids we find four main differences: (i) the memory kernel contains Umklapp processes, (ii) besides the static two-molecule orientational correlators one also needs the static one-molecule orientational density as an input, where the latter is nontrivial, (iii) the static orientational current density correlator does contribute an anisotropic, inertia-independent part to the memory kernel, (iv) if the molecules are assumed to be fixed on a rigid lattice, the tensorial orientational correlators and the memory kernel have …
Low-energy fixed points of random Heisenberg models
2002
The effect of quenched disorder on the low-energy and low-temperature properties of various two- and three-dimensional Heisenberg models is studied by a numerical strong disorder renormalization group method. For strong enough disorder we have identified two relevant fixed points, in which the gap exponent, omega, describing the low-energy tail of the gap distribution, P(Delta) ~ Delta^omega is independent of disorder, the strength of couplings and the value of the spin. The dynamical behavior of non-frustrated random antiferromagnetic models is controlled by a singlet-like fixed point, whereas for frustrated models the fixed point corresponds to a large spin formation and the gap exponent …
Numerical tests of conjectures of conformal field theory for three-dimensional systems
1999
The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables, one thus obtains not only the critical exponents but even the corresponding amplitudes of the divergences analytically. A first numerical analysis brought up the question whether analogous results can be obtained for those systems on three-dimensional manifolds. Using Monte Carlo simulations based on the Wolff single-cluster update algorithm we investigate the scaling properties of O(n) symmetric classical spin models on a three-dimensional, hyper-cylindr…