1,666 research outputs found
Transport coefficients of multi-particle collision algorithms with velocity-dependent collision rules
Detailed calculations of the transport coefficients of a recently introduced
particle-based model for fluid dynamics with a non-ideal equation of state are
presented. Excluded volume interactions are modeled by means of biased
stochastic multiparticle collisions which depend on the local velocities and
densities. Momentum and energy are exactly conserved locally. A general scheme
to derive transport coefficients for such biased, velocity dependent collision
rules is developed. Analytic expressions for the self-diffusion coefficient and
the shear viscosity are obtained, and very good agreement is found with
numerical results at small and large mean free paths. The viscosity turns out
to be proportional to the square root of temperature, as in a real gas. In
addition, the theoretical framework is applied to a two-component version of
the model, and expressions for the viscosity and the difference in diffusion of
the two species are given.Comment: 31 pages, 8 figures, accepted by J. Phys. Cond. Matte
Mesoscopic model for the fluctuating hydrodynamics of binary and ternary mixtures
A recently introduced particle-based model for fluid dynamics with continuous
velocities is generalized to model immiscible binary mixtures. Excluded volume
interactions between the two components are modeled by stochastic multiparticle
collisions which depend on the local velocities and densities. Momentum and
energy are conserved locally, and entropically driven phase separation occurs
for high collision rates. An explicit expression for the equation of state is
derived, and the concentration dependence of the bulk free energy is shown to
be the same as that of the Widom-Rowlinson model. Analytic results for the
phase diagram are in excellent agreement with simulation data. Results for the
line tension obtained from the analysis of the capillary wave spectrum of a
droplet agree with measurements based on the Laplace's equation. The
introduction of "amphiphilic" dimers makes it possible to model the phase
behavior and dynamics of ternary surfactant mixtures.Comment: 7 pages including 6 figure
Thermodynamics of the frustrated - Heisenberg ferromagnet on the body-centered cubic lattice with arbitrary spin
We use the spin-rotation-invariant Green's function method as well as the
high-temperature expansion to discuss the thermodynamic properties of the
frustrated spin- - Heisenberg magnet on the body-centered
cubic lattice. We consider ferromagnetic nearest-neighbor bonds and
antiferromagnetic next-nearest-neighbor bonds and arbitrary spin
. We find that the transition point between the ferromagnetic ground
state and the antiferromagnetic one is nearly independent of the spin ,
i.e., it is very close to the classical transition point . At finite temperatures we focus on the parameter regime
with a ferromagnetic ground-state. We calculate the Curie
temperature and derive an empirical formula describing the
influence of the frustration parameter and spin on . We find
that the Curie temperature monotonically decreases with increasing frustration
, where very close to the -curve exhibits a
fast decay which is well described by a logarithmic term
. To characterize the magnetic ordering
below and above , we calculate the spin-spin correlation functions
, the spontaneous
magnetization, the uniform static susceptibility as well as the
correlation length . Moreover, we discuss the specific heat and the
temperature dependence of the excitation spectrum. As approaching the
transition point some unusual features were found, such as negative
spin-spin correlations at temperatures above even though the ground state
is ferromagnetic or an increase of the spin stiffness with growing temperature.Comment: 19 pages, 10 figures, version as in EPJ
Thermodynamics of the one-dimensional frustrated Heisenberg ferromagnet with arbitrary spin
The thermodynamic quantities (spin-spin correlation functions <{\bf S}_0{\bf
S}_n>, correlation length {\xi}, spin susceptibility {\chi}, and specific heat
C_V) of the frustrated one-dimensional J1-J2 Heisenberg ferromagnet with
arbitrary spin quantum number S below the quantum critical point, i.e. for J2<
|J1|/4, are calculated using a rotation-invariant Green-function formalism and
full diagonalization as well as a finite-temperature Lanczos technique for
finite chains of up to N=18 sites. The low-temperature behavior of the
susceptibility {\chi} and the correlation length {\xi} is well described by
\chi = (2/3)S^4 (|J1|-4J2) T^{-2} + A S^{5/2} (|J1|-4J2)^{1/2} T^{-3/2} and \xi
= S^2 (|J1|-4J2) T^{-1} + B S^{1/2} (|J1|-4J2)^{1/2} T^{-1/2} with A \approx
1.1 ... 1.2 and B \approx 0.84 ... 0.89. The vanishing of the factors in front
of the temperature at J2=|J1|/4 indicates a change of the critical behavior of
{\chi} and {\xi} at T \to 0. The specific heat may exhibit an additional
frustration-induced low-temperature maximum when approaching the quantum
critical point. This maximum appears for S=1/2 and S=1, but was not found for
S>1.Comment: 8 pages, 7 figure
Green's function theory of quasi-two-dimensional spin-half Heisenberg ferromagnets: stacked square versus stacked kagom\'e lattice
We consider the thermodynamic properties of the quasi-two-dimensional
spin-half Heisenberg ferromagnet on the stacked square and the stacked kagom\'e
lattices by using the spin-rotation-invariant Green's function method. We
calculate the critical temperature , the uniform static susceptibility
, the correlation lengths and the magnetization and
investigate the short-range order above . We find that and at
are smaller for the stacked kagom\'e lattice which we attribute to
frustration effects becoming relevant at finite temperatures.Comment: shortened version as published in PR
Quantum -- antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
Using the coupled-cluster method (CCM) and the rotation-invariant Green's
function method (RGM), we study the influence of the interlayer coupling
on the magnetic ordering in the ground state of the spin-1/2
- frustrated Heisenberg antiferromagnet (- model) on the
stacked square lattice. In agreement with known results for the -
model on the strictly two-dimensional square lattice () we find that
the phases with magnetic long-range order at small and large
are separated by a magnetically disordered (quantum
paramagnetic) ground-state phase. Increasing the interlayer coupling
the parameter region of this phase decreases, and, finally, the
quantum paramagnetic phase disappears for quite small .Comment: 4 pages, 3 figure
Electron-hole pair condensation at the semimetal-semiconductor transition: a BCS-BEC crossover scenario
We act on the suggestion that an excitonic insulator state might
separate---at very low temperatures---a semimetal from a semiconductor and ask
for the nature of these transitions. Based on the analysis of electron-hole
pairing in the extended Falicov-Kimball model, we show that tuning the Coulomb
attraction between both species, a continuous crossover between a BCS-like
transition of Cooper-type pairs and a Bose-Einstein condensation of preformed
tightly-bound excitons might be achieved in a solid-state system. The precursor
of this crossover in the normal state might cause the transport anomalies
observed in several strongly correlated mixed-valence compounds.Comment: 5 pages, 5 figures, substantially revised versio
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