2,192 research outputs found
Random walks on finite lattice tubes
Exact results are obtained for random walks on finite lattice tubes with a
single source and absorbing lattice sites at the ends. Explicit formulae are
derived for the absorption probabilities at the ends and for the expectations
that a random walk will visit a particular lattice site before being absorbed.
Results are obtained for lattice tubes of arbitrary size and each of the
regular lattice types; square, triangular and honeycomb. The results include an
adjustable parameter to model the effects of strain, such as surface curvature,
on the surface diffusion. Results for the triangular lattice tubes and the
honeycomb lattice tubes model diffusion of adatoms on single walled zig-zag
carbon nano-tubes with open ends.Comment: 22 pages, 4 figure
Exact Results for Hamiltonian Walks from the Solution of the Fully Packed Loop Model on the Honeycomb Lattice
We derive the nested Bethe Ansatz solution of the fully packed O() loop
model on the honeycomb lattice. From this solution we derive the bulk free
energy per site along with the central charge and geometric scaling dimensions
describing the critical behaviour. In the limit we obtain the exact
compact exponents and for Hamiltonian walks, along with
the exact value for the connective constant
(entropy). Although having sets of scaling dimensions in common, our results
indicate that Hamiltonian walks on the honeycomb and Manhattan lattices lie in
different universality classes.Comment: 12 pages, RevTeX, 3 figures supplied on request, ANU preprint
MRR-050-9
Magnetic Correlation Length and Universal Amplitude of the Lattice E_8 Ising Model
The perturbation approach is used to derive the exact correlation length
of the dilute A_L lattice models in regimes 1 and 2 for L odd. In regime
2 the A_3 model is the E_8 lattice realisation of the two-dimensional Ising
model in a magnetic field h at T=T_c. When combined with the singular part f_s
of the free energy the result for the A_3 model gives the universal amplitude
as in precise agreement with the result
obtained by Delfino and Mussardo via the form-factor bootstrap approach.Comment: 7 pages, Late
Path Crossing Exponents and the External Perimeter in 2D Percolation
2D Percolation path exponents describe probabilities for
traversals of annuli by non-overlapping paths, each on either occupied
or vacant clusters, with at least one of each type. We relate the probabilities
rigorously to amplitudes of models whose exponents, believed to be
exact, yield . This extends to half-integers
the Saleur--Duplantier exponents for clusters, yields the exact
fractal dimension of the external cluster perimeter, , and also explains the absence of narrow gate fjords, as originally
found by Grossman and Aharony.Comment: 4 pages, 2 figures (EPSF). Revised presentatio
Inertial range scaling in numerical turbulence with hyperviscosity
Numerical turbulence with hyperviscosity is studied and compared with direct
simulations using ordinary viscosity and data from wind tunnel experiments. It
is shown that the inertial range scaling is similar in all three cases.
Furthermore, the bottleneck effect is approximately equally broad (about one
order of magnitude) in these cases and only its height is increased in the
hyperviscous case--presumably as a consequence of the steeper decent of the
spectrum in the hyperviscous subrange. The mean normalized dissipation rate is
found to be in agreement with both wind tunnel experiments and direct
simulations. The structure function exponents agree with the She-Leveque model.
Decaying turbulence with hyperviscosity still gives the usual t^{-1.25} decay
law for the kinetic energy, and also the bottleneck effect is still present and
about equally strong.Comment: Final version (7 pages
Recommended from our members
Fleeing from a little bit of water: A very ‘Un-Roman’ response to changing environmental constraints. A case study from Monteux, Southern France
Variational approach to the scaling function of the 2D Ising model in a magnetic field
The universal scaling function of the square lattice Ising model in a
magnetic field is obtained numerically via Baxter's variational corner transfer
matrix approach. The high precision numerical data is in perfect agreement with
the remarkable field theory results obtained by Fonseca and Zamolodchikov, as
well as with many previously known exact and numerical results for the 2D Ising
model. This includes excellent agreement with analytic results for the magnetic
susceptibility obtained by Orrick, Nickel, Guttmann and Perk. In general the
high precision of the numerical results underlines the potential and full power
of the variational corner transfer matrix approach.Comment: 12 pages, 1 figure, 4 tables, v2: minor corrections, references adde
Decay of scalar turbulence revisited
We demonstrate that at long times the rate of passive scalar decay in a
turbulent, or simply chaotic, flow is dominated by regions (in real space or in
inverse space) where mixing is less efficient. We examine two situations. The
first is of a spatially homogeneous stationary turbulent flow with both viscous
and inertial scales present. It is shown that at large times scalar
fluctuations decay algebraically in time at all spatial scales (particularly in
the viscous range, where the velocity is smooth). The second example explains
chaotic stationary flow in a disk/pipe. The boundary region of the flow
controls the long-time decay, which is algebraic at some transient times, but
becomes exponential, with the decay rate dependent on the scalar diffusion
coefficient, at longer times.Comment: 4 pages, no figure
Conformational Entropy of Compact Polymers
Exact results for the scaling properties of compact polymers on the square
lattice are obtained from an effective field theory. The entropic exponent
\gamma=117/112 is calculated, and a line of fixed points associated with
interacting chains is identified; along this line \gamma varies continuously.
Theoretical results are checked against detailed numerical transfer matrix
calculations, which also yield a precise estimate for the connective constant
\kappa=1.47280(1).Comment: 4 pages, 1 figur
Bethe Ansatz study of one-dimensional Bose and Fermi gases with periodic and hard wall boundary conditions
We extend the exact periodic Bethe Ansatz solution for one-dimensional bosons
and fermions with delta-interaction and arbitrary internal degrees of freedom
to the case of hard wall boundary conditions. We give an analysis of the ground
state properties of fermionic systems with two internal degrees of freedom,
including expansions of the ground state energy in the weak and strong coupling
limits in the repulsive and attractive regimes.Comment: 27 pages, 6 figures, key reference added, typos correcte
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