625 research outputs found
Lattice theory of finite-size effects above the upper critical dimension
We present a perturbative calculation of finite-size effects near of
the lattice model in a -dimensional cubic geometry of size with
periodic boundary conditions for . The structural differences between
the lattice theory and the field theory found previously in
the spherical limit are shown to exist also for a finite number of components
of the order parameter. The two-variable finite-size scaling functions of the
field theory are nonuniversal whereas those of the lattice theory are
independent of the nonuniversal model parameters.One-loop results for
finite-size scaling functions are derived. Their structure disagrees with the
single-variable scaling form of the lowest-mode approximation for any finite
where is the bulk correlation length. At , the large-
behavior becomes lowest-mode like for the lattice model but not for the
field-theoretic model. Characteristic temperatures close to of the
lattice model, such as of the maximum of the susceptibility
, are found to scale asymptotically as ,
in agreement with previous Monte Carlo (MC) data for the five-dimensional Ising
model. We also predict asymptotically. On a
quantitative level, the asymptotic amplitudes of this large - behavior close
to have not been observed in previous MC simulations at because
of nonnegligible finite-size terms caused by the
inhomogeneous modes. These terms identify the possible origin of a significant
discrepancy between the lowest-mode approximation and previous MC data. MC data
of larger systems would be desirable for testing the magnitude of the
and terms predicted by our theory.Comment: Accepted in Int. J. Mod. Phys.
Global Persistence Exponent in Critical Dynamics: Finite Size induced Crossover
We extend the definition of a global order parameter to the case of a
critical system confined between two infinite parallel plates separated by a
finite distance . For a quench to the critical point we study the
persistence property of the global order parameter and show that there is a
crossover behaviour characterized by a non universal exponent which depends on
the ratio of the system size to a dynamic length scale
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
Critical Behavior of O(n)-symmetric Systems With Reversible Mode-coupling Terms: Stability Against Detailed-balance Violation
We investigate nonequilibrium critical properties of -symmetric models
with reversible mode-coupling terms. Specifically, a variant of the model of
Sasv\'ari, Schwabl, and Sz\'epfalusy is studied, where violation of detailed
balance is incorporated by allowing the order parameter and the dynamically
coupled conserved quantities to be governed by heat baths of different
temperatures and , respectively. Dynamic perturbation theory and the
field-theoretic renormalization group are applied to one-loop order, and yield
two new fixed points in addition to the equilibrium ones. The first one
corresponds to and leads to model A critical
behavior for the order parameter and to anomalous noise correlations for the
generalized angular momenta; the second one is at and is
characterized by mean-field behavior of the conserved quantities, by a dynamic
exponent equal to that of the equilibrium SSS model, and by
modified static critical exponents. However, both these new fixed points are
unstable, and upon approaching the critical point detailed balance is restored,
and the equilibrium static and dynamic critical properties are recovered.Comment: 18 pages, RevTeX, 1 figure included as eps-file; submitted to Phys.
Rev.
Scaling of thermal conductivity of helium confined in pores
We have studied the thermal conductivity of confined superfluids on a
bar-like geometry. We use the planar magnet lattice model on a lattice with . We have applied open boundary conditions on the bar
sides (the confined directions of length ) and periodic along the long
direction. We have adopted a hybrid Monte Carlo algorithm to efficiently deal
with the critical slowing down and in order to solve the dynamical equations of
motion we use a discretization technique which introduces errors only
in the time step . Our results demonstrate the
validity of scaling using known values of the critical exponents and we
obtained the scaling function of the thermal resistivity. We find that our
results for the thermal resistivity scaling function are in very good agreement
with the available experimental results for pores using the tempComment: 5 two-column pages, 3 figures, Revtex
Five-loop additive renormalization in the phi^4 theory and amplitude functions of the minimally renormalized specific heat in three dimensions
We present an analytic five-loop calculation for the additive renormalization
constant A(u,epsilon) and the associated renormalization-group function B(u) of
the specific heat of the O(n) symmetric phi^4 theory within the minimal
subtraction scheme. We show that this calculation does not require new
five-loop integrations but can be performed on the basis of the previous
five-loop calculation of the four-point vertex function combined with an
appropriate identification of symmetry factors of vacuum diagrams. We also
determine the amplitude functions of the specific heat in three dimensions for
n=1,2,3 above T_c and for n=1 below T_c up to five-loop order. Accurate results
are obtained from Borel resummations of B(u) for n=1,2,3 and of the amplitude
functions for n=1. Previous conjectures regarding the smallness of the resummed
higher-order contributions are confirmed. Borel resummed universal amplitude
ratios A^+/A^- and a_c^+/a_c^- are calculated for n=1.Comment: 30 pages REVTeX, 3 PostScript figures, submitted to Phys. Rev.
New Geologic Map of the Argyre Region of Mars
The new generation of Mars orbital topographic and imaging data justifies a new mapping effort of the Argyre impact basin and surroundings (-30.0deg to -65.0deg lat., -20.0deg to -70.0deg long; Fig.1). Our primary objective is to produce a geologic map of the Argyre region at 1:5,000,000 scale in both digital and print formats. The map will detail the stratigraphic and crosscutting relations among rock materials and landforms. These include Argyre basin infill, impact crater rim materials and adjoining highland materials of Noachis Terra, valleys and elongated basins that are radial and concentric about the primary Argyre basin, faults, enigmatic ridges, lobate debris aprons, and valley networks. Such information will be useful to the planetary science community for constraining the regional geology, paleohydrology, and paleoclimate. This includes the assessment of: (a) whether the Argyre basin contained lakes [1], (b) the extent of reported flooding and glaciation, which includes ancient flows of volatiles into the impact basin [2-4], (c) existing interpretations of the origin of the narrow ridges located in the southeast part of the basin floor [2,5], and (d) the extent of Argyre-related tectonism and its influence on the surrounding regions. Whereas the geologic mapping investigation of Timothy Parker focuses on the Argyre floor materials at 1:1,000,000 (MTMs -50036, -50043, -55036, -55043; see Fig. 1 for approximate corners of the area), our regional geologic mapping investigation includes the Argyre basin floor and rim materials, the transition zone that straddles the Thaumasia plateau, which includes Argyre impact-related modification [6], and the southeast margin of the Thaumasia plateau using important new data sets (Fig. 1). Our mapping effort will incorporate the map information of Parker if it is made available during the project
Geologic controls of erosion and sedimentation on Mars
Because Mars has had a history of diverse erosional and depositional styles, a variety of erosional landforms and sedimentary deposits can be seen on Viking orbiter images. Here we review how geologic processes involving rock, water, and structure have controlled erosion and sedimentation on Mars. Additionally, we review how further studies will help refine our understanding of these processes
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