478 research outputs found
Static and Dynamic Critical Behavior of a Symmetrical Binary Fluid: A Computer Simulation
A symmetrical binary, A+B Lennard-Jones mixture is studied by a combination
of semi-grandcanonical Monte Carlo (SGMC) and Molecular Dynamics (MD) methods
near a liquid-liquid critical temperature . Choosing equal chemical
potentials for the two species, the SGMC switches identities () to generate well-equilibrated configurations of the system on
the coexistence curve for and at the critical concentration, ,
for . A finite-size scaling analysis of the concentration susceptibility
above and of the order parameter below is performed, varying the
number of particles from N=400 to 12800. The data are fully compatible with the
expected critical exponents of the three-dimensional Ising universality class.
The equilibrium configurations from the SGMC runs are used as initial states
for microcanonical MD runs, from which transport coefficients are extracted.
Self-diffusion coefficients are obtained from the Einstein relation, while the
interdiffusion coefficient and the shear viscosity are estimated from
Green-Kubo expressions. As expected, the self-diffusion constant does not
display a detectable critical anomaly. With appropriate finite-size scaling
analysis, we show that the simulation data for the shear viscosity and the
mutual diffusion constant are quite consistent both with the theoretically
predicted behavior, including the critical exponents and amplitudes, and with
the most accurate experimental evidence.Comment: 35 pages, 13 figure
Critical Dynamics in a Binary Fluid: Simulations and Finite-size Scaling
We report comprehensive simulations of the critical dynamics of a symmetric
binary Lennard-Jones mixture near its consolute point. The self-diffusion
coefficient exhibits no detectable anomaly. The data for the shear viscosity
and the mutual-diffusion coefficient are fully consistent with the asymptotic
power laws and amplitudes predicted by renormalization-group and mode-coupling
theories {\it provided} finite-size effects and the background contribution to
the relevant Onsager coefficient are suitably accounted for. This resolves a
controversy raised by recent molecular simulations.Comment: 4 pages, 4 figure
Low temperature expansion for the 3-d Ising Model
We compute the weak coupling expansion for the energy of the three
dimensional Ising model through 48 excited bonds. We also compute the
magnetization through 40 excited bonds. This was achieved via a recursive
enumeration of states of fixed energy on a set of finite lattices. We use a
linear combination of lattices with a generalization of helical boundary
conditions to eliminate finite volume effects.Comment: 10 pages, IASSNS-HEP-92/42, BNL-4767
Series expansions without diagrams
We discuss the use of recursive enumeration schemes to obtain low and high
temperature series expansions for discrete statistical systems. Using linear
combinations of generalized helical lattices, the method is competitive with
diagramatic approaches and is easily generalizable. We illustrate the approach
using the Ising model and generate low temperature series in up to five
dimensions and high temperature series in three dimensions. The method is
general and can be applied to any discrete model. We describe how it would work
for Potts models.Comment: 24 pages, IASSNS-HEP-93/1
The Conical Point in the Ferroelectric Six-Vertex Model
We examine the last unexplored regime of the asymmetric six-vertex model: the
low-temperature phase of the so-called ferroelectric model. The original
publication of the exact solution, by Sutherland, Yang, and Yang, and various
derivations and reviews published afterwards, do not contain many details about
this regime. We study the exact solution for this model, by numerical and
analytical methods. In particular, we examine the behavior of the model in the
vicinity of an unusual coexistence point that we call the ``conical'' point.
This point corresponds to additional singularities in the free energy that were
not discussed in the original solution. We show analytically that in this point
many polarizations coexist, and that unusual scaling properties hold in its
vicinity.Comment: 28 pages (LaTeX); 8 postscript figures available on request
([email protected]). Submitted to Journal of Statistical Physics. SFU-DJBJDS-94-0
Nonequilibrium stationary states and equilibrium models with long range interactions
It was recently suggested by Blythe and Evans that a properly defined steady
state normalisation factor can be seen as a partition function of a fictitious
statistical ensemble in which the transition rates of the stochastic process
play the role of fugacities. In analogy with the Lee-Yang description of phase
transition of equilibrium systems, they studied the zeroes in the complex plane
of the normalisation factor in order to find phase transitions in
nonequilibrium steady states. We show that like for equilibrium systems, the
``densities'' associated to the rates are non-decreasing functions of the rates
and therefore one can obtain the location and nature of phase transitions
directly from the analytical properties of the ``densities''. We illustrate
this phenomenon for the asymmetric exclusion process. We actually show that its
normalisation factor coincides with an equilibrium partition function of a walk
model in which the ``densities'' have a simple physical interpretation.Comment: LaTeX, 23 pages, 3 EPS figure
Non exponential relaxation in fully frustrated models
We study the dynamical properties of the fully frustrated Ising model. Due to
the absence of disorder the model, contrary to spin glass, does not exhibit any
Griffiths phase, which has been associated to non-exponential relaxation
dynamics. Nevertheless we find numerically that the model exhibits a stretched
exponential behavior below a temperature T_p corresponding to the percolation
transition of the Kasteleyn-Fortuin clusters. We have also found that the
critical behavior of this clusters for a fully frustrated q-state spin model at
the percolation threshold is strongly affected by frustration. In fact while in
absence of frustration the q=1 limit gives random percolation, in presence of
frustration the critical behavior is in the same universality class of the
ferromagnetic q=1/2-state Potts model.Comment: 7 pages, RevTeX, 11 figs, to appear on Physical Review
Metastable States in Spin Glasses and Disordered Ferromagnets
We study analytically M-spin-flip stable states in disordered short-ranged
Ising models (spin glasses and ferromagnets) in all dimensions and for all M.
Our approach is primarily dynamical and is based on the convergence of a
zero-temperature dynamical process with flips of lattice animals up to size M
and starting from a deep quench, to a metastable limit. The results (rigorous
and nonrigorous, in infinite and finite volumes) concern many aspects of
metastable states: their numbers, basins of attraction, energy densities,
overlaps, remanent magnetizations and relations to thermodynamic states. For
example, we show that their overlap distribution is a delta-function at zero.
We also define a dynamics for M=infinity, which provides a potential tool for
investigating ground state structure.Comment: 34 pages (LaTeX); to appear in Physical Review
Qudi: a modular python suite for experiment control and data processing
Qudi is a general, modular, multi-operating system suite written in Python 3
for controlling laboratory experiments. It provides a structured environment by
separating functionality into hardware abstraction, experiment logic and user
interface layers. The core feature set comprises a graphical user interface,
live data visualization, distributed execution over networks, rapid prototyping
via Jupyter notebooks, configuration management, and data recording. Currently,
the included modules are focused on confocal microscopy, quantum optics and
quantum information experiments, but an expansion into other fields is possible
and encouraged. Qudi is available from https://github.com/Ulm-IQO/qudi and is
freely useable under the GNU General Public Licence.Comment: Software paper, 9 pages, 2 figure
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