1,350 research outputs found
Exact solution and surface critical behaviour of open cyclic SOS lattice models
We consider the -state cyclic solid-on-solid lattice models under a class
of open boundary conditions. The integrable boundary face weights are obtained
by solving the reflection equations. Functional relations for the fused
transfer matrices are presented for both periodic and open boundary conditions.
The eigen-spectra of the unfused transfer matrix is obtained from the
functional relations using the analytic Bethe ansatz. For a special case of
crossing parameter , the finite-size corrections to the
eigen-spectra of the critical models are obtained, from which the corresponding
conformal dimensions follow. The calculation of the surface free energy away
from criticality yields two surface specific heat exponents,
and , where
coprime to . These results are in agreement with the scaling relations
and .Comment: 13 pages, LaTeX, to appear in J. Phys.
Model of the meniscus of an ionic liquid ion source.
A simple model of the transfer of charge and ion evaporation in the meniscus of an ionic-liquid ion source working in the purely ionic regime is proposed on the basis of order-of-magnitude estimates which show that, in this regime, _i_ the flow in the meniscus is dominated by the viscosity of the liquid and is affected very little by the mass flux accompanying ion evaporation, and _ii_ the effect of the space charge around the evaporating surface is negligible and the evaporation current is controlled by the finite electrical conductivity of the liquid. The model predicts that a stationary meniscus of a very polar liquid undergoing ion evaporation is nearly hydrostatic and can exist only below a certain value of the applied electric field, at which the meniscus attains its maximum elongation but stays smooth. The electric current vs applied electric field characteristic displays a frozen regime of negligible ion evaporation at low fields and a conduction-controlled regime at higher fields, with a sharp transition between the two regimes owing to the high sensitivity of the ion evaporation rate to the electric field. A simplified treatment of the flow in the capillary or liquid layer through which liquid is delivered to the meniscus shows that the size of the meniscus decreases and the maximum attainable current increases when the feeding pressure is decreased, and that appropriate combinations of feeding pressure and pressure drop may lead to high maximum currents
Thermal and magnetic properties of integrable spin-1 and spin-3/2 chains with applications to real compounds
The ground state and thermodynamic properties of spin-1 and spin-3/2 chains
are investigated via exactly solved su(3) and su(4) models with physically
motivated chemical potential terms. The analysis involves the Thermodynamic
Bethe Ansatz and the High Temperature Expansion (HTE) methods. For the spin-1
chain with large single-ion anisotropy, a gapped phase occurs which is
significantly different from the valence-bond-solid Haldane phase. The
theoretical curves for the magnetization, susceptibility and specific heat are
favourably compared with experimental data for a number of spin-1 chain
compounds. For the spin-3/2 chain a degenerate gapped phase exists starting at
zero external magnetic field. A middle magnetization plateau can be triggered
by the single-ion anisotropy term. Overall, our results lend further weight to
the applicability of integrable models to the physics of low-dimensional
quantum spin systems. They also highlight the utility of the exact HTE method.Comment: 38 pages, 15 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
The XXZ model with anti-periodic twisted boundary conditions
We derive functional equations for the eigenvalues of the XXZ model subject
to anti-diagonal twisted boundary conditions by means of fusion of transfer
matrices and by Sklyanin's method of separation of variables. Our findings
coincide with those obtained using Baxter's method and are compared to the
recent solution of Galleas. As an application we study the finite size scaling
of the ground state energy of the model in the critical regime.Comment: 22 pages and 3 figure
Relative dispersion in fully developed turbulence: The Richardson's Law and Intermittency Corrections
Relative dispersion in fully developed turbulence is investigated by means of
direct numerical simulations. Lagrangian statistics is found to be compatible
with Richardson description although small systematic deviations are found. The
value of the Richardson constant is estimated as , in a close
agreement with recent experimental findings [S. Ott and J. Mann J. Fluid Mech.
{\bf 422}, 207 (2000)]. By means of exit-time statistics it is shown that the
deviations from Richardson's law are a consequence of Eulerian intermittency.
The measured Lagrangian scaling exponents require a set of Eulerian structure
function exponents which are remarkably close to standard ones
known for fully developed turbulence
Inverse lift: a signature of the elasticity of complex fluids?
To understand the mechanics of a complex fluid such as a foam we propose a
model experiment (a bidimensional flow around an obstacle) for which an
external sollicitation is applied, and a local response is measured,
simultaneously. We observe that an asymmetric obstacle (cambered airfoil
profile) experiences a downards lift, opposite to the lift usually known (in a
different context) in aerodynamics. Correlations of velocity, deformations and
pressure fields yield a clear explanation of this inverse lift, involving the
elasticity of the foam. We argue that such an inverse lift is likely common to
complex fluids with elasticity.Comment: 4 pages, 4 figures, revised version, submitted to PR
Magnus and Iordanskii Forces in Superfluids
The total transverse force acting on a quantized vortex in a superfluid is a
problem that has eluded a complete understanding for more than three decades.
In this letter I propose a remarkably simple argument, somewhat reminiscent of
Laughlin's beautiful argument for the quantization of conductance in the
quantum Hall effect, to define the superfluid velocity part of the transverse
force. This term is found to be . Although
this result does not seem to be overly controversial, this thermodynamic
argument based only on macroscopic properties of the superfluid does offer a
robust derivation. A recent publication by Thouless, Ao and Niu has
demonstrated that the vortex velocity part of the transverse force in a
homogeneous neutral superfluid is given by the usual form . A combination of these two independent results and the required
Galilean invariance yields that there cannot be any transverse force
proportional to the normal fluid velocity, in apparent conflict with
Iordanskii's theory of the transverse force due to phonon scattering by the
vortex.Comment: RevTex, 1 Encapsulated Postscript figur
Magnetization Plateaus in a Solvable 3-Leg Spin Ladder
We present a solvable ladder model which displays magnetization plateaus at
fractional values of the total magnetization. Plateau signatures are also shown
to exist along special lines. The model has isotropic Heisenberg interactions
with additional many-body terms. The phase diagram can be calculated exactly
for all values of the rung coupling and the magnetic field. We also derive the
anomalous behaviour of the susceptibility near the plateau boundaries. There is
good agreement with the phase diagram obtained recently for the pure Heisenberg
ladders by numerical and perturbative techniques.Comment: 4 pages, revtex, 3 postscript figures, small changes to the text and
references update
Normal and Anomalous Scaling of the Fourth-Order Correlation Function of a Randomly Advected Passive Scalar
For a delta-correlated velocity field, simultaneous correlation functions of
a passive scalar satisfy closed equations. We analyze the equation for the
four-point function. To describe a solution completely, one has to solve the
matching problems at the scale of the source and at the diffusion scale. We
solve both the matching problems and thus find the dependence of the four-point
correlation function on the diffusion and pumping scale for large space
dimensionality . It is shown that anomalous scaling appears in the first
order of perturbation theory. Anomalous dimensions are found analytically
both for the scalar field and for it's derivatives, in particular, for the
dissipation field.Comment: 19 pages, RevTex 3.0, Submitted to Phys.Rev. E, revised versio
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