2,177 research outputs found
Some comments on developments in exact solutions in statistical mechanics since 1944
Lars Onsager and Bruria Kaufman calculated the partition function of the
Ising model exactly in 1944 and 1949. Since then there have been many
developments in the exact solution of similar, but usually more complicated,
models. Here I shall mention a few, and show how some of the latest work seems
to be returning once again to the properties observed by Onsager and Kaufman.Comment: 28 pages, 5 figures, section on six-vertex model revise
Electroviscous effects of simple electrolytes under shear
On the basis of a hydrodynamical model analogous to that in critical fluids,
we investigate the influences of shear flow upon the electrostatic contribution
to the viscosity of binary electrolyte solutions in the Debye-H\"{u}ckel
approximation. Within the linear-response theory, we reproduce the classical
limiting law that the excess viscosity is proportional to the square root of
the concentration of the electrolyte. We also extend this result for finite
shear. An analytic expression of the anisotropic structure factor of the charge
density under shear is obtained, and its deformation at large shear rates is
discussed. A non-Newtonian effect caused by deformations of the ionic
atmosphere is also elucidated for . This finding
concludes that the maximum shear stress that the ionic atmosphere can support
is proportional to , where , and
are, respectively, the shear rate, the Debye screening
length and the Debye relaxation time with being the relative diffusivity at
the infinite dilution limit of the electrolyte.Comment: 13pages, 2figure
Entropy-driven formation of the gyroid cubic phase
We show, by computer simulation, that tapered or pear-shaped particles, interacting through purely repulsive interactions, can freely self-assemble to form the three-dimensionally periodic, gyroid cubic phase. The Ia3d gyroid cubic phase is formed by these particles both on compression of an isotropic configuration and on expansion of a smectic A bilayer arrangement. For the latter case, it is possible identify the steps by which the topological transformation from non-intersecting planes to fully interpenetrating, periodic networks takes place</p
Storage Capacity of Two-dimensional Neural Networks
We investigate the maximum number of embedded patterns in the two-dimensional
Hopfield model. The grand state energies of two specific network states,
namely, the energies of the pure-ferromagnetic state and the state of specific
one stored pattern are calculated exactly in terms of the correlation function
of the ferromagnetic Ising model. We also investigate the energy landscape
around them by computer simulations. Taking into account the qualitative
features of the phase diagrams obtained by Nishimori, Whyte and Sherrington
[Phys. Rev. E {\bf 51}, 3628 (1995)], we conclude that the network cannot
retrieve more than three patterns.Comment: 13pages, 7figures, revtex
Using the de Haas-van Alphen effect to map out the closed three-dimensional Fermi surface of natural graphite
The Fermi surface of graphite has been mapped out using de Haas van Alphen
(dHvA) measurements at low temperature with in-situ rotation. For tilt angles
between the magnetic field and the c-axis, the majority
electron and hole dHvA periods no longer follow the behavior
demonstrating that graphite has a 3 dimensional closed Fermi surface. The Fermi
surface of graphite is accurately described by highly elongated ellipsoids. A
comparison with the calculated Fermi surface suggests that the SWM trigonal
warping parameter is significantly larger than previously thought
Corner transfer matrices in statistical mechanics
Corner transfer matrices are a useful tool in the statistical mechanics of
simple two-dimensinal models. They can be very effective way of obtaining
series expansions of unsolved models, and of calculating the order parameters
of solved ones. Here we review these features and discuss the reason why the
method fails to give the order parameter of the chiral Potts model.Comment: 18 pages, 4 figures, for Proceedings of Conference on Symmetries and
Integrability of Difference Equations. (SIDE VII), Melbourne, July 200
Correlation energy of an electron gas: a functional approach
Correlation effects of an electron gas in an external potential are derived
using an Effective Action functional method. Corrections beyond the random
phase approximation (RPA) are naturally incorporated by this method. The
Effective Action functional is made to depend explicitly on two-point
correlation functions. The calculation is carried out at imaginary time. For a
homogeneous electron gas, we calculate the effect of exchange on the ring
diagrams at zero temperature and show how to include some of the ladder
diagrams. Our results agree well with known numerical calculations. We conclude
by showing that this method is in fact a variant of the time dependent density
functional method and suggest that it is suitable to be applied to the study of
correlation effects in the non-homogeneous case.Comment: 20 figures numbered as in the tex
Island formation without attractive interactions
We show that adsorbates on surfaces can form islands even if there are no
attractive interactions. Instead strong repulsion between adsorbates at short
distances can lead to islands, because such islands increase the entropy of the
adsorbates that are not part of the islands. We suggest that this mechanism
cause the observed island formation in O/Pt(111), but it may be important for
many other systems as well.Comment: 11 pages, 4 figure
Quantum macrostatistical picture of nonequilibrium steady states
We employ a quantum macrostatistical treatment of irreversible processes to
prove that, in nonequilibrium steady states, (a) the hydrodynamical observables
execute a generalised Onsager-Machlup process and (b) the spatial correlations
of these observables are generically of long range. The key assumptions behind
these results are a nonequilibrium version of Onsager's regression hypothesis,
together with certain hypotheses of chaoticity and local equilibrium for
hydrodynamical fluctuations.Comment: TeX, 13 page
Hard colloidal rods near a soft wall: wetting, drying, and symmetry breaking
Within an Onsager-like density functional theory we explore the thermodynamic
and structural properties of an isotropic and nematic fluid of hard needle-like
colloids in contact with a hard substrate coated with a soft short-ranged
attractive or repulsive layer. As a function of the range and the strength of
the soft interactions we find wetting and drying transitions, a pre-drying
line, and a symmetry-breaking transition from uniaxial to biaxial in the
wetting and drying film.Comment: 7 pages, 2 figure
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