290 research outputs found
Non-universal size dependence of the free energy of confined systems near criticality
The singular part of the finite-size free energy density of the O(n)
symmetric field theory in the large-n limit is calculated at finite
cutoff for confined geometries of linear size L with periodic boundary
conditions in 2 < d < 4 dimensions. We find that a sharp cutoff
causes a non-universal leading size dependence
near which dominates the universal scaling term . This
implies a non-universal critical Casimir effect at and a leading
non-scaling term of the finite-size specific heat above .Comment: RevTex, 4 page
Fluctuation force exerted by a planar self-avoiding polymer
Using results from Schramm Loewner evolution (SLE), we give the expression of
the fluctuation-induced force exerted by a polymer on a small impenetrable
disk, in various 2-dimensional domain geometries. We generalize to two polymers
and examine whether the fluctuation force can trap the object into a stable
equilibrium. We compute the force exerted on objects at the domain boundary,
and the force mediated by the polymer between such objects. The results can
straightforwardly be extended to any SLE interface, including Ising,
percolation, and loop-erased random walks. Some are relevant for extremal value
statistics.Comment: 7 pages, 22 figure
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
Nonuniversal finite-size scaling in anisotropic systems
We study the bulk and finite-size critical behavior of the O symmetric
theory with spatially anisotropic interactions of non-cubic symmetry
in dimensions. In such systems of a given universality class,
two-scale factor universality is absent in bulk correlation functions, and
finite-size scaling functions including the Privman-Fisher scaling form of the
free energy, the Binder cumulant ratio and the Casimir amplitude are shown to
be nonuniversal. In particular it is shown that, for anisotropic confined
systems, isotropy cannot be restored by an anisotropic scale transformation.Comment: 8 pages, 1 figure, accepted for publication in Phys. Rev. E and
modifications of tex
THEORY OF PHASE-LOCKING IN SMALL JOSEPHSON JUNCTION CELLS
Within the RSJ model, we performed a theoretical analysis of phase-locking in
elementary strongly coupled Josephson junction cells. For this purpose, we
developed a systematic method allowing the investigation of phase-locking in
cells with small but non-vanishing loop inductance.The voltages across the
junctions are found to be locked with very small phase difference for almost
all values of external flux. However, the general behavior of phase-locking is
found to be just contrary to that according to weak coupling. In case of strong
coupling there is nearly no influence of external magnetic flux on the phases,
but the locking-frequency becomes flux-dependent. The influence of parameter
splitting is considered as well as the effect of small capacitive shunting of
the junctions. Strongly coupled cells show synchronization even for large
parameter splitting. Finally, a study of the behavior under external microwave
radiation shows that the frequency locking-range becomes strongly
flux-dependent, whereas the locking frequency itself turns out to be
flux-independent.Comment: 26 pages, REVTEX, 9 PS figures appended in uuencoded form at the end,
submitted to Phys. Rev. B
Dynamic Critical Behavior of the Heisenberg Model with Strong Easy Plane Anisotropy
The dynamic critical behavior of the Heisenberg model with a strong
anisotropy of the exchange constant in the z direction is investigated. The
main features of the time evolution of this model are revealed. The static and
dynamic critical behavior of planar magnetic models is shown to be described
well by the Heisenberg model with strong easy plane anisotropy.Comment: 5 pages, 4 figures, 1 tabl
Critical free energy and Casimir forces in rectangular geometries
We study the critical behavior of the free energy and the thermodynamic
Casimir force in a block geometry in
dimensions with aspect ratio above, at, and below on
the basis of the O symmetric lattice model with periodic boundary
conditions (b.c.). We consider a simple-cubic lattice with isotropic
short-range interactions. Exact results are derived in the large - limit
describing the geometric crossover from film () over cubic to
cylindrical () geometries. For , three perturbation
approaches are presented that cover both the central finite-size regime near
for and the region outside the central
finite-size regime well above and below for arbitrary . At bulk
of isotropic systems with periodic b.c., we predict the critical Casimir
force in the vertical direction to be negative (attractive) for a slab
(), and zero for a cube
. We also present extrapolations to the cylinder limit
() and to the film limit () for and . Our
analytic results for finite-size scaling functions in the minimal
renormalization scheme at fixed dimension agree well with Monte Carlo
data for the three-dimensional Ising model by Hasenbusch for and by
Vasilyev et al. for above, at, and below .Comment: 23 pages, 14 figure
Universality of the thermodynamic Casimir effect
Recently a nonuniversal character of the leading spatial behavior of the
thermodynamic Casimir force has been reported [X. S. Chen and V. Dohm, Phys.
Rev. E {\bf 66}, 016102 (2002)]. We reconsider the arguments leading to this
observation and show that there is no such leading nonuniversal term in systems
with short-ranged interactions if one treats properly the effects generated by
a sharp momentum cutoff in the Fourier transform of the interaction potential.
We also conclude that lattice and continuum models then produce results in
mutual agreement independent of the cutoff scheme, contrary to the
aforementioned report. All results are consistent with the {\em universal}
character of the Casimir force in systems with short-ranged interactions. The
effects due to dispersion forces are discussed for systems with periodic or
realistic boundary conditions. In contrast to systems with short-ranged
interactions, for one observes leading finite-size contributions
governed by power laws in due to the subleading long-ranged character of
the interaction, where is the finite system size and is the
correlation length.Comment: 11 pages, revtex, to appear in Phys. Rev. E 68 (2003
Local functional models of critical correlations in thin-films
Recent work on local functional theories of critical inhomogeneous fluids and
Ising-like magnets has shown them to be a potentially exact, or near exact,
description of universal finite-size effects associated with the excess
free-energy and scaling of one-point functions in critical thin films. This
approach is extended to predict the two-point correlation function G in
critical thin-films with symmetric surface fields in arbitrary dimension d. In
d=2 we show there is exact agreement with the predictions of conformal
invariance for the complete spectrum of correlation lengths as well as the
detailed position dependence of the asymptotic decay of G. In d=3 and d>=4 we
present new numerical predictions for the universal finite-size correlation
length and scaling functions determining the structure of G across the
thin-film. Highly accurate analytical closed form expressions for these
universal properties are derived in arbitrary dimension.Comment: 4 pages, 1 postscript figure. Submitted to Phys Rev Let
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