2,705 research outputs found
An Onsager-like Relation for the Lattice Boltzmann Method
An Onsager-like relation is proposed as a new criterion for constructing and
analysing the lattice Boltzmann (LB) method. For LB models obeying the
relation, we analyse their linearized stability, establish their diffusive
limit, and find new constraints for those with free parameters. The new
relation seems of fundamental importance for the LB method.Comment: 4 page
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
Duality and Symmetry in Chiral Potts Model
We discover an Ising-type duality in the general -state chiral Potts
model, which is the Kramers-Wannier duality of planar Ising model when N=2.
This duality relates the spectrum and eigenvectors of one chiral Potts model at
a low temperature (of small ) to those of another chiral Potts model at a
high temperature (of ). The -model and chiral Potts model
on the dual lattice are established alongside the dual chiral Potts models.
With the aid of this duality relation, we exact a precise relationship between
the Onsager-algebra symmetry of a homogeneous superintegrable chiral Potts
model and the -loop-algebra symmetry of its associated
spin- XXZ chain through the identification of their eigenstates.Comment: Latex 34 pages, 2 figures; Typos and misprints in Journal version are
corrected with minor changes in expression of some formula
Universality in phase boundary slopes for spin glasses on self dual lattices
We study the effects of disorder on the slope of the disorder--temperature
phase boundary near the Onsager point (Tc = 2.269...) in spin-glass models. So
far, studies have focused on marginal or irrelevant cases of disorder. Using
duality arguments, as well as exact Pfaffian techniques we reproduce these
analytical estimates. In addition, we obtain different estimates for spin-glass
models on hierarchical lattices where the effects of disorder are relevant. We
show that the phase-boundary slope near the Onsager point can be used to probe
for the relevance of disorder effects.Comment: 8 pages, 6 figure
The challenge of the chiral Potts model
The chiral Potts model continues to pose particular challenges in statistical
mechanics: it is ``exactly solvable'' in the sense that it satisfies the
Yang-Baxter relation, but actually obtaining the solution is not easy. Its free
energy was calculated in 1988 and the order parameter was conjectured in full
generality a year later.
However, a derivation of that conjecture had to wait until 2005. Here we
discuss that derivation.Comment: 22 pages, 3 figures, 29 reference
The Onsager Algebra Symmetry of -matrices in the Superintegrable Chiral Potts Model
We demonstrate that the -matrices in the superintegrable chiral
Potts model possess the Onsager algebra symmetry for their degenerate
eigenvalues. The Fabricius-McCoy comparison of functional relations of the
eight-vertex model for roots of unity and the superintegrable chiral Potts
model has been carefully analyzed by identifying equivalent terms in the
corresponding equations, by which we extract the conjectured relation of
-operators and all fusion matrices in the eight-vertex model corresponding
to the -relation in the chiral Potts model.Comment: Latex 21 pages; Typos added, References update
Three dimensional hysdrodynamic lattice-gas simulations of binary immiscible and ternary amphiphilic flow through porous media
We report the results of a study of multiphase flow in porous media. A
Darcy's law for steady multiphase flow was investigated for both binary and
ternary amphiphilic flow. Linear flux-forcing relationships satisfying Onsager
reciprocity were shown to be a good approximation of the simulation data. The
dependence of the relative permeability coefficients on water saturation was
investigated and showed good qualitative agreement with experimental data.
Non-steady state invasion flows were investigated, with particular interest in
the asymptotic residual oil saturation. The addition of surfactant to the
invasive fluid was shown to significantly reduce the residual oil saturation.Comment: To appear in Phys. Rev.
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