771 research outputs found
Surface scaling behavior of isotropic Heisenberg systems: Critical exponents, structure factor, and profiles
The surface scaling behavior of classical isotropic Heisenberg magnets is
investigated by Monte - Carlo methods in d=3 dimensions for various values of
the surface - to - bulk coupling ratio J_1/J. For J_1/J <= 1.0 critical
behavior according to the ordinary surface universality class is found. New
estimates for magnetic surface exponents are presented and compared to older
estimates and their theoretical counterparts. For J_1/J >= 2.0 scaling is still
valid with effective exponents which depend on J_1/J. The surface structure
factor S_1(p,L) is investigated at bulk criticality as function of the momentum
transfer p parallel to the surface and the system size L. For J_1/J <= 1.0 and
J_1/J >= 2.0 the full p dependence of S_1(p,L) can be captured by generalized
shape functions to a remarkable accuracy. Profiles of the magnetization and the
energy density also confirm scaling, where for J_1/J <= 1.0 the ordinary
surface universality class is recovered and for J_1/J >= 2.0 scaling with J_1/J
dependent exponents is found. For J_1/J = 1.5 the system displays a striking
crossover behavior from spurious long - range surface order to the ordinary
surface universality class. For J_1/J >= 2.0 the effective scaling laws must be
interpreted as nonasymptotic and the value J_1/J = 1.5 marks a crossover
regime, in which the crossover from the nonasymptotic to the asymptotic
(ordinary) surface scaling behavior can be resolved within numerically
attainable system sizes.Comment: 14 pages RevTeX, 14 figures; to appear in Phys. Rev. B, Sept. 200
Anti-phase locking in a two-dimensional Josephson junction array
We consider theoretically phase locking in a simple two-dimensional Josephson
junction array consisting of two loops coupled via a joint line transverse to
the bias current. Ring inductances are supposed to be small, and special
emphasis is taken on the influence of external flux. Is is shown, that in the
stable oscillation regime both cells oscillate with a phase shift equal to
(i.e. anti-phase). This result may explain the low radiation output
obtained so far in two-dimensional Josephson junction arrays experimentally.Comment: 11 pages, REVTeX, 1 Postscript figure, Subm. to Appl. Phys. Let
Critical Casimir Effect in 3He-4He films
Universal aspects of the thermodynamic Casimir effect in wetting films of
3He-4He mixtures near their bulk tricritical point are studied within suitable
models serving as representatives of the corresponding universality class. The
effective forces between the boundaries of such films arising from the
confinement are calculated along isotherms at several fixed concentrations of
3He. Nonsymmetric boundary conditions impose nontrivial concentration profiles
leading to repulsive Casimir forces which exhibit a rich behavior of the
crossover between the tricritical point and the line of critical points. The
theoretical results agree with published experimental data and emphasize the
importance of logarithmic corrections.Comment: 12 pages, 4 figures, submitted to the Phys. Rev. Let
Phase diagram of a model for 3He-4He mixtures in three dimensions
A lattice model of 3He - 4He mixtures which takes into account the continuous
rotational symmetry O(2) of the superfluid degrees of freedom of 4He is studied
in the molecular-field approximation and by Monte Carlo simulations in three
dimensions. In contrast to its two-dimensional version, for reasonable values
of the interaction parameters the resulting phase diagram resembles that
observed experimentally for 3He - 4He mixtures, for which phase separation
occurs as a consequence of the superfluid transition. The corresponding
continuum Ginzburg-Landau model with two order parameters describing 3He- 4He
mixtures near tricriticality is derived from the considered lattice model. All
coupling constants appearing in the continuum model are explicitly expressed in
terms of the mean concentration of 4He, the temperature, and the microscopic
interaction parameters characterizing the lattice system.Comment: 32 pages, 12 figures, submitted to the Phys. Rev.
The coil-globule transition of confined polymers
We study long polymer chains in a poor solvent, confined to the space between
two parallel hard walls. The walls are energetically neutral and pose only a
geometric constraint which changes the properties of the coil-globule (or
"-") transition. We find that the temperature increases
monotonically with the width between the walls, in contrast to recent
claims in the literature. Put in a wider context, the problem can be seen as a
dimensional cross over in a tricritical point of a model. We roughly
verify the main scaling properties expected for such a phenomenon, but we find
also somewhat unexpected very long transients before the asymptotic scaling
regions are reached. In particular, instead of the expected scaling exactly at the (-dependent) theta point we found that increases
less fast than , even for extremely long chains.Comment: 5 pages, 6 figure
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
Dynamic surface critical behavior of isotropic Heisenberg ferromagnets: boundary conditions, renormalized field theory, and computer simulation results
The dynamic critical behavior of isotropic Heisenberg ferromagnets with a
planar free surface is investigated by means of field-theoretic renormalization
group techniques and high-precision computer simulations. An appropriate
semi-infinite extension of the stochastic model J is constructed. The relevant
boundary terms of the action of the associated dynamic field theory are
identified, the implied boundary conditions are derived, and the
renormalization of the model in bulk dimensions is clarified. Two
distinct renormalization schemes are utilized. The first is a massless one
based on minimal subtraction of dimensional poles and the dimensionality
expansion about . To overcome its problems in going below
dimensions, a massive one for fixed dimensions is constructed. The
resulting renormalization group (or Callan Symanzik) equations are exploited to
obtain the scaling forms of surface quantities like the dynamic structure
factor. In conjunction with boundary operator expansions scaling relations
follow that relate the critical indices of the dynamic and static infrared
singularities of surface quantities to familiar \emph{static} bulk and surface
exponents. To test the predicted scaling forms and scaling-law expressions for
the critical exponents involved, accurate computer-simulation data are
presented for the dynamic surface structure factor. These are in conformity
with our predictions.Comment: Revtex4-file with 4 figures included as eps-files, 21 pages in
print-format, typos corrected, to appear in Phys. Rev. B, July
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
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
Effective forces between colloids at interfaces induced by capillary wave-like fluctuations
We calculate the effective force mediated by thermally excited capillary
waves between spherical or disklike colloids trapped at a fluid interface. This
Casimir type interaction is shown to depend sensitively on the boundary
conditions imposed at the three-phase contact line. For large distances between
the colloids an unexpected cancellation of attractive and repulsive
contributions is observed leading to a fluctuation force which decays
algebraically very rapidly. For small separations the resulting force is rather
strong and it may play an important role in two-dimensional colloid aggregation
if direct van der Waals forces are weak.Comment: 7 pages, 3 figures, minor revisions, one additional figur
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