30 research outputs found
Critical Casimir forces along the iso-fields
Using quasi-exact numerical density-matrix renormalization-group techniques
we calculate the critical Casimir force for a two-dimensional (2D) Ising strip
with equal strong surface fields, along the thermodynamic paths corresponding
to the fixed nonzero bulk field h0. Using the Derjaguin approximation we also
determine the critical Casimir force and its potential for two discs. We find
that varying the temperature along the iso-fields lying between the bulk
coexistence and the capillary condensation critical point leads to a dramatic
increase of the critical Casimir interactions with a qualitatively different
functional dependence on the temperature than along h=0. These findings might
be of relevance for biomembranes, whose heterogeneity is recently interpreted
as being connected with a critical behavior belonging to the 2D Ising
universality class.Comment: 9 pages, 12 figures, submitted to Physical Review
Solvation force for long ranged wall-fluid potentials
The solvation force of a simple fluid confined between identical planar walls
is studied in two model systems with short ranged fluid-fluid interactions and
long ranged wall-fluid potentials decaying as , for
various values of . Results for the Ising spins system are obtained in two
dimensions at vanishing bulk magnetic field by means of the
density-matrix renormalization-group method; results for the truncated
Lennard-Jones (LJ) fluid are obtained within the nonlocal density functional
theory. At low temperatures the solvation force for the Ising film
is repulsive and decays for large wall separations in the same fashion as
the boundary field , whereas for temperatures larger than
the bulk critical temperature is attractive and the asymptotic decay
is . For the LJ fluid system is always
repulsive away from the critical region and decays for large with the the
same power law as the wall-fluid potential. We discuss the influence of the
critical Casimir effect and of capillary condensation on the behaviour of the
solvation force.Comment: 48 pages, 12 figure
Solvation forces in Ising films with long-range boundary fields: density-matrix renormalization-group study
Using the quasi-exact density-matrix renormalization-group method we
calculate the solvation forces in two-dimensional Ising films of thickness L
subject to identical algebraically decaying boundary fields with various decay
exponents p. At the bulk critical point the solvation force acquires a
universal contribution which is long-ranged in L due to the critical
fluctuations, a phenomenon known as the critical Casimir effect. For p = 2, 3
and 50, we study the scaling behaviour of the solvation force along the
pseudo-phase coexistence and along the critical and sub-critical isotherms.Comment: 9 pages, 6 figures, accepted to Molecular Physic
Influence of Capillary Condensation on the Near-Critical Solvation Force
We argue that in a fluid, or magnet, confined by adsorbing walls which favour
liquid, or (+) phase, the solvation (Casimir) force in the vicinity of the
critical point is strongly influenced by capillary condensation which occurs
below the bulk critical temperature T_c. At T slightly below and above T_c, a
small bulk field h<0, which favours gas, or (-) phase, leads to residual
condensation and a solvation force which is much more attractive (at the same
large wall separation) than that found exactly at the critical point. Our
predictions are supported by results obtained from density-matrix
renormalization-group calculations in a two-dimensional Ising strip subject to
identical surface fields.Comment: 4 Pages, RevTeX, and 3 figures include
Density Matrix Renormalization Group of Gapless Systems
We investigate convergence of the density matrix renormalization group (DMRG)
in the thermodynamic limit for gapless systems. Although the DMRG correlations
always decay exponentially in the thermodynamic limit, the correlation length
at the DMRG fixed-point scales as , where is the number
of kept states, indicating the existence of algebraic order for the exact
system. The single-particle excitation spectrum is calculated, using a
Bloch-wave ansatz, and we prove that the Bloch-wave ansatz leads to the
symmetry for translationally invariant half-integer
spin-systems with local interactions. Finally, we provide a method to compute
overlaps between ground states obtained from different DMRG calculations.Comment: 11 pages, RevTex, 5 figure
Effect of Gravity and Confinement on Phase Equilibria: A Density Matrix Renormalization Approach
The phase diagram of the 2D Ising model confined between two infinite walls
and subject to opposing surface fields and to a bulk "gravitational" field is
calculated by means of density matrix renormalization methods. In absence of
gravity two phase coexistence is restricted to temperatures below the wetting
temperature. We find that gravity restores the two phase coexistence up to the
bulk critical temperature, in agreement with previous mean-field predictions.
We calculate the exponents governing the finite size scaling in the temperature
and in the gravitational field directions. The former is the exponent which
describes the shift of the critical temperature in capillary condensation. The
latter agrees, for large surface fields, with a scaling assumption of Van
Leeuwen and Sengers. Magnetization profiles in the two phase and in the single
phase region are calculated. The profiles in the single phase region, where an
interface is present, agree well with magnetization profiles calculated from a
simple solid-on-solid interface hamiltonian.Comment: 4 pages, RevTeX and 4 PostScript figures included. Final version as
published. To appear in Phys. Rev. Let
Interplay of complete wetting, critical adsorption, and capillary condensation
The excess adsorption in two-dimensional Ising strips subject to identical boundary fields, at both one-dimensional
surfaces decaying in the orthogonal direction as , is studied
for various values of and along various thermodynamic paths below the
critical point by means of the density-matrix renormalization-group method. The
crossover behavior between the complete wetting and critical adsorption
regimes, occurring in semi-infinite systems, are strongly influenced by
confinement effects. Along isotherms the asymptotic power law
dependences on the external bulk field, which characterize these two regimes,
are undercut by capillary condensation. Along the pseudo first-order phase
coexistence line of the strips, which varies with temperature, we find a broad
crossover regime where both the thickness of the wetting film and
increase as function of the reduced temperature but do not follow any
power law. Above the wetting temperature the order parameter profiles are not
slab-like but exhibit wide interfacial variations and pronounced tails. Inter
alia, our explicit calculations demonstrate that, contrary to opposite claims
by Kroll and Lipowsky [Phys. Rev. B {\bf 28}, 5273 (1983)], for critical
wetting transitions do exist and we determine the corresponding wetting phase
diagram in the plane.Comment: RevTeX 23 Pages and 17 figures, submitted to Phys. Rev.