2,987 research outputs found
Crossover from Goldstone to critical fluctuations: Casimir forces in confined O symmetric systems
We study the crossover between thermodynamic Casimir forces arising from
long-range fluctuations due to Goldstone modes and those arising from critical
fluctuations. Both types of forces exist in the low-temperature phase of O
symmetric systems for in a -dimensional
slab geometry with a finite aspect ratio . Our
finite-size renormalization-group treatment for periodic boundary conditions
describes the entire crossover from the Goldstone regime with a nonvanishing
constant tail of the finite-size scaling function far below up to the
region far above including the critical regime with a minimum of the
scaling function slightly below . Our analytic result for
agrees well with Monte Carlo data for the three-dimensional XY model. A
quantitative prediction is given for the crossover of systems in the Heisenberg
universality class.Comment: 2 figure
Pronounced minimum of the thermodynamic Casimir forces of O() symmetric film systems: Analytic theory
Thermodynamic Casimir forces of film systems in the O universality
classes with Dirichlet boundary conditions are studied below bulk criticality.
Substantial progress is achieved in resolving the long-standing problem of
describing analytically the pronounced minimum of the scaling function observed
experimentally in He films by R. Garcia and M.H.W. Chan, Phys. Rev.
Lett. and in Monte Carlo simulations for the
three-dimensional Ising model () by O. Vasilyev et al., EPL . Our finite-size renormalization-group approach yields
excellent agreement with the depth and the position of the minimum for
and semiquantitative agreement with the minimum for . Our theory also
predicts a pronounced minimum for the Heisenberg universality class.Comment: 1 figur
Critical Casimir force in slab geometry with finite aspect ratio: analytic calculation above and below
We present a field-theoretic study of the critical Casimir force of the Ising
universality class in a -dimensional slab
geometry with a finite aspect ratio above, at, and below
. The result of a perturbation approach at fixed dimension is
presented that describes the dependence on the aspect ratio in the range . Our analytic result for the Casimir force scaling function for
agrees well with recent Monte Carlo data for the three-dimensional
Ising model in slab geometry with periodic boundary conditions above, at, and
below .Comment: 4 figure
Minimal renormalization without \epsilon-expansion: Three-loop amplitude functions of the O(n) symmetric \phi^4 model in three dimensions below T_c
We present an analytic three-loop calculation for thermodynamic quantities of
the O(n) symmetric \phi^4 theory below T_c within the minimal subtraction
scheme at fixed dimension d=3. Goldstone singularities arising at an
intermediate stage in the calculation of O(n) symmetric quantities cancel among
themselves leaving a finite result in the limit of zero external field. From
the free energy we calculate the three-loop terms of the amplitude functions
f_phi, F+ and F- of the order parameter and the specific heat above and below
T_c, respectively, without using the \epsilon=4-d expansion. A Borel
resummation for the case n=2 yields resummed amplitude functions f_phi and F-
that are slightly larger than the one-loop results. Accurate knowledge of these
functions is needed for testing the renormalization-group prediction of
critical-point universality along the \lambda-line of superfluid He(4).
Combining the three-loop result for F- with a recent five-loop calculation of
the additive renormalization constant of the specific heat yields excellent
agreement between the calculated and measured universal amplitude ratio A+/A-
of the specific heat of He(4). In addition we use our result for f_phi to
calculate the universal combination R_C of the amplitudes of the order
parameter, the susceptibility and the specific heat for n=2 and n=3. Our
Borel-resummed three-loop result for R_C is significantly more accurate than
the previous result obtained from the \epsilon-expansion up to O(\epsilon^2).Comment: 29 pages LaTeX including 3 PostScript figures, to appear in Nucl.
Phys. B [FS] (1998
Minimal renormalization without epsilon-expansion: Amplitude functions in three dimensions below T_c
Massive field theory at fixed dimension d<4 is combined with the minimal
subtraction scheme to calculate the amplitude functions of thermodynamic
quantities for the O(n) symmetric phi^4 model below T_c in two-loop order.
Goldstone singularities arising at an intermediate stage in the calculation of
O(n) symmetric quantities are shown to cancel among themselves leaving a finite
result in the limit of zero external field. From the free energy we calculate
the amplitude functions in zero field for the order parameter, specific heat
and helicity modulus (superfluid density) in three dimensions. We also
calculate the q^2 part of the inverse of the wavenumber-dependent transverse
susceptibility chi_T(q) which provides an independent check of our result for
the helicity modulus. The two-loop contributions to the superfluid density and
specific heat below T_c turn out to be comparable in magnitude to the one-loop
contributions, indicating the necessity of higher-order calculations and
Pade-Borel type resummations.Comment: 41 pages, LaTeX, 8 PostScript figures, submitted to NPB [FS
Finite-size effects on the thermal conductivity of ^4He near T_\lambda
We present results of a renormalization-group calculation of the thermal
conductivity of confined He in a geometry above and
at within model F with Dirichlet boundary conditions for the order
parameter. We assume a heat flow parallel to the boundaries which implies
Neumann boundary conditions for the entropy density. No adjustable parameters
other than those known from bulk theory and static finite-size theory are used.
Our theoretical results are compared with experimental data by Kahn and Ahlers.Comment: 2 pages, 2 figure
Implicitization of Bihomogeneous Parametrizations of Algebraic Surfaces via Linear Syzygies
We show that the implicit equation of a surface in 3-dimensional projective
space parametrized by bi-homogeneous polynomials of bi-degree (d,d), for a
given positive integer d, can be represented and computed from the linear
syzygies of its parametrization if the base points are isolated and form
locally a complete intersection
Violation of Finite-Size Scaling in Three Dimensions
We reexamine the range of validity of finite-size scaling in the
lattice model and the field theory below four dimensions. We show that
general renormalization-group arguments based on the renormalizability of the
theory do not rule out the possibility of a violation of finite-size
scaling due to a finite lattice constant and a finite cutoff. For a confined
geometry of linear size with periodic boundary conditions we analyze the
approach towards bulk critical behavior as at fixed for where is the bulk correlation length. We show that for this
analysis ordinary renormalized perturbation theory is sufficient. On the basis
of one-loop results and of exact results in the spherical limit we find that
finite-size scaling is violated for both the lattice model and the
field theory in the region . The non-scaling effects in the
field theory and in the lattice model differ significantly from each other.Comment: LaTex, 51 page
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