7 research outputs found
Model fluid in a porous medium: results for a Bethe lattice
We consider a lattice gas with quenched impurities or `quenched-annealed
binary mixture' on the Bethe lattice. The quenched part represents a porous
matrix in which the (annealed) lattice gas resides. This model features the 3
main factors of fluids in random porous media: wetting, randomness and
confinement. The recursive character of the Bethe lattice enables an exact
treatment, whose key ingredient is an integral equation yielding the
one-particle effective field distribution. Our analysis shows that this
distribution consists of two essentially different parts. The first one is a
continuous spectrum and corresponds to the macroscopic volume accessible to the
fluid, the second is discrete and comes from finite closed cavities in the
porous medium. Those closed cavities are in equilibrium with the bulk fluid
within the grand canonical ensemble we use, but are inaccessible in real
experimental situations. Fortunately, we are able to isolate their
contributions. Separation of the discrete spectrum facilitates also the
numerical solution of the main equation. The numerical calculations show that
the continuous spectrum becomes more and more rough as the temperature
decreases, and this limits the accuracy of the solution at low temperatures.Comment: 13 pages, 12 figure
Bulk and Boundary Critical Behavior at Lifshitz Points
Lifshitz points are multicritical points at which a disordered phase, a
homogeneous ordered phase, and a modulated ordered phase meet. Their bulk
universality classes are described by natural generalizations of the standard
model. Analyzing these models systematically via modern
field-theoretic renormalization group methods has been a long-standing
challenge ever since their introduction in the middle of the 1970s. We survey
the recent progress made in this direction, discussing results obtained via
dimensionality expansions, how they compare with Monte Carlo results, and open
problems. These advances opened the way towards systematic studies of boundary
critical behavior at -axial Lifshitz points. The possible boundary critical
behavior depends on whether the surface plane is perpendicular to one of the
modulation axes or parallel to all of them. We show that the semi-infinite
field theories representing the corresponding surface universality classes in
these two cases of perpendicular and parallel surface orientation differ
crucially in their Hamiltonian's boundary terms and the implied boundary
conditions, and explain recent results along with our current understanding of
this matter.Comment: Invited contribution to STATPHYS 22, to be published in the
Proceedings of the 22nd International Conference on Statistical Physics
(STATPHYS 22) of the International Union of Pure and Applied Physics (IUPAP),
4--9 July 2004, Bangalore, Indi
Critical behavior at m-axial Lifshitz points: field-theory analysis and -expansion results
The critical behavior of d-dimensional systems with an n-component order
parameter is reconsidered at (m,d,n)-Lifshitz points, where a wave-vector
instability occurs in an m-dimensional subspace of . Our aim is
to sort out which ones of the previously published partly contradictory
-expansion results to second order in are
correct. To this end, a field-theory calculation is performed directly in the
position space of dimensions, using dimensional
regularization and minimal subtraction of ultraviolet poles. The residua of the
dimensionally regularized integrals that are required to determine the series
expansions of the correlation exponents and and of the
wave-vector exponent to order are reduced to single
integrals, which for general m=1,...,d-1 can be computed numerically, and for
special values of m, analytically. Our results are at variance with the
original predictions for general m. For m=2 and m=6, we confirm the results of
Sak and Grest [Phys. Rev. B {\bf 17}, 3602 (1978)] and Mergulh{\~a}o and
Carneiro's recent field-theory analysis [Phys. Rev. B {\bf 59},13954 (1999)].Comment: Latex file with one figure (eps-file). Latex file uses texdraw to
generate figures that are included in the tex
Landau theory of phase transitions in TTF-TCNQ
Several parameters of the Landau Free Energy Function of TTF-TCNQ are calculated from the crystal structure taking into account the atomic positions and realistic charge distributions. In particular, the parameters that determine the coupling between charge density waves and rotations (librons) on neighbouring chains are evaluated. The Free Energy Function is solved, and good agreement with the experimental observation of the 2 a period between 53 K and 48 K and its variation below this temperature, is obtained. The CDW-libron interaction seems to be responsible for this transverse period. The behaviour of C p in the vicinity of the two close phase transitions is studied. The Free Energy should possess several (up to four) Lifshitz points, for appropriate values of the parameters.On calcule plusieurs paramètres de l'énergie libre de Landau pour TTF-TCNQ à partir de la structure cristalline en tenant compte de la position des atomes et des distributions de charge réalistes. En particulier, on évalue les paramètres qui déterminent le couplage entre les ondes de densité de charge et les rotations (librons) sur des chaînes voisines. On résoud la fonction d'énergie libre et on obtient un bon accord avec l'observation expérimentale de la période 2 a entre 53 K et 48 K et sa variation en dessous de cette température. L'interaction « onde de densité de charge »-libron semble être responsable pour cette période transversale. On étudie le comportement de Cp aux environs des deux transitions de phases voisines. L'énergie libre devrait avoir plusieurs (jusqu'a quatre) points de Lifshitz, pour des valeurs convenables des paramètres