495 research outputs found
Field-Theoretical Analysis of Critical and Coexistence Singularities at Critical End Points
Continuum models with critical end points are considered whose Hamiltonian
depends on two densities and .
Field-theoretic methods are used to show the equivalence of the critical
behavior on the critical line and at the critical end point and to give a
systematic derivation of critical-end-point singularities like the thermal
singularity of the spectator-phase boundary and the
coexistence singularities or of the
secondary density . The appearance of a discontinuity eigenexponent
associated with the critical end point is confirmed, and the mechanism by which
it arises in field theory is clarified.Comment: Latex2e file using elsart stylefile, no figures. submitted to
Proceedings of Statphys Taipei-99, to be published in Physica
Boundary critical behavior at m-axial Lifshitz points for a boundary plane parallel to the modulation axes
The critical behavior of semi-infinite -dimensional systems with
-component order parameter and short-range interactions is
investigated at an -axial bulk Lifshitz point whose wave-vector instability
is isotropic in an -dimensional subspace of . The associated
modulation axes are presumed to be parallel to the surface, where . An appropriate semi-infinite model representing the
corresponding universality classes of surface critical behavior is introduced.
It is shown that the usual O(n) symmetric boundary term
of the Hamiltonian must be supplemented by one of the form involving a
dimensionless (renormalized) coupling constant . The implied boundary
conditions are given, and the general form of the field-theoretic
renormalization of the model below the upper critical dimension
is clarified. Fixed points describing the ordinary, special,
and extraordinary transitions are identified and shown to be located at a
nontrivial value if . The surface
critical exponents of the ordinary transition are determined to second order in
. Extrapolations of these expansions yield values of these
exponents for in good agreement with recent Monte Carlo results for the
case of a uniaxial () Lifshitz point. The scaling dimension of the surface
energy density is shown to be given exactly by , where
is the anisotropy exponent.Comment: revtex4, 31 pages with eps-files for figures, uses texdraw to
generate some graphs; to appear in PRB; v2: some references and additional
remarks added, labeling in figure 1 and some typos correcte
Analytic Solution of Emden-Fowler Equation and Critical Adsorption in Spherical Geometry
In the framework of mean-field theory the equation for the order-parameter
profile in a spherically-symmetric geometry at the bulk critical point reduces
to an Emden-Fowler problem. We obtain analytic solutions for the surface
universality class of extraordinary transitions in for a spherical shell,
which may serve as a starting point for a pertubative calculation. It is
demonstrated that the solution correctly reproduces the Fisher-de Gennes effect
in the limit of the parallel-plate geometry.Comment: (to be published in Z. Phys. B), 7 pages, 1 figure, uuencoded
postscript file, 8-9
Dynamic surface scaling behavior of isotropic Heisenberg ferromagnets
The effects of free surfaces on the dynamic critical behavior of isotropic
Heisenberg ferromagnets are studied via phenomenological scaling theory,
field-theoretic renormalization group tools, and high-precision computer
simulations. An appropriate semi-infinite extension of the stochastic model J
is constructed, the boundary terms of the associated dynamic field theory are
identified, its renormalization in d <= 6 dimensions is clarified, and the
boundary conditions it satisfies are given. Scaling laws are derived which
relate the critical indices of the dynamic and static infrared singularities of
surface quantities to familiar static bulk and surface exponents. Accurate
computer-simulation data are presented for the dynamic surface structure
factor; these are in conformity with the predicted scaling behavior and could
be checked by appropriate scattering experiments.Comment: 9 pages, 2 figure
Dynamical Relaxation and Universal Short-Time Behavior in Finite Systems: The Renormalization Group Approach
We study how the finite-sized n-component model A with periodic boundary
conditions relaxes near its bulk critical point from an initial nonequilibrium
state with short-range correlations. Particular attention is paid to the
universal long-time traces that the initial condition leaves. An approach based
on renormalization-group improved perturbation theory in 4-epsilon space
dimensions and a nonperturbative treatment of the q=0 mode of the fluctuating
order-parameter field is developed. This leads to a renormalized effective
stochastic equation for this mode in the background of the other q=0 modes; we
explicitly derive it to one-loop order, show that it takes the expected
finite-size scaling form at the fixed point, and solve it numerically. Our
results confirm for general n that the amplitude of the magnetization density
m(t) in the linear relaxation-time regime depends on the initial magnetization
in the universal fashion originally found in our large- analysis [J.\ Stat.
Phys. 73 (1993) 1]. The anomalous short-time power-law increase of m(t) also is
recovered. For n=1, our results are in fair agreement with recent Monte Carlo
simulations by Li, Ritschel, and Zheng [J. Phys. A 27 (1994) L837] for the
three-dimensional Ising model.Comment: 27 pages, 7 postscript figures, REVTEX 3.0, submitted to Nucl. Phys.
Ising cubes with enhanced surface couplings
Using Monte Carlo techniques, Ising cubes with ferromagnetic nearest-neighbor
interactions and enhanced couplings between surface spins are studied. In
particular, at the surface transition, the corner magnetization shows
non-universal, coupling-dependent critical behavior in the thermodynamic limit.
Results on the critical exponent of the corner magnetization are compared to
previous findings on two-dimensional Ising models with three intersecting
defect lines.Comment: 4 pages, 2 figures included, submitted to Phys. Rev.
Critical Casimir amplitudes for -component models with O(n)-symmetry breaking quadratic boundary terms
Euclidean -component theories whose Hamiltonians are O(n)
symmetric except for quadratic symmetry breaking boundary terms are studied in
films of thickness . The boundary terms imply the Robin boundary conditions
at the boundary
planes at and . Particular attention is paid
to the cases in which of the variables
take the special value corresponding to critical
enhancement while the remaining ones are subcritically enhanced. Under these
conditions, the semi-infinite system bounded by has a
multicritical point, called -special, at which an symmetric
critical surface phase coexists with the O(n) symmetric bulk phase, provided
is sufficiently large. The -dependent part of the reduced free energy
per area behaves as as at the bulk critical
point. The Casimir amplitudes are determined for small
in the general case where components are
critically enhanced at both boundary planes, components are
enhanced at one plane but satisfy asymptotic Dirichlet boundary conditions at
the respective other, and the remaining components satisfy asymptotic
Dirichlet boundary conditions at both . Whenever ,
these expansions involve integer and fractional powers with
(mod logarithms). Results to for general values of
, , and are used to estimate the
of 3D Heisenberg systems with surface spin anisotropies when , , and .Comment: Latex source file with 5 eps files; version with minor amendments and
corrected typo
Topological Defects, Orientational Order, and Depinning of the Electron Solid in a Random Potential
We report on the results of molecular dynamics simulation (MD) studies of the
classical two-dimensional electron crystal in the presence disorder. Our study
is motivated by recent experiments on this system in modulation doped
semiconductor systems in very strong magnetic fields, where the magnetic length
is much smaller than the average interelectron spacing , as well as by
recent studies of electrons on the surface of helium. We investigate the low
temperature state of this system using a simulated annealing method. We find
that the low temperature state of the system always has isolated dislocations,
even at the weakest disorder levels investigated. We also find evidence for a
transition from a hexatic glass to an isotropic glass as the disorder is
increased. The former is characterized by quasi-long range orientational order,
and the absence of disclination defects in the low temperature state, and the
latter by short range orientational order and the presence of these defects.
The threshold electric field is also studied as a function of the disorder
strength, and is shown to have a characteristic signature of the transition.
Finally, the qualitative behavior of the electron flow in the depinned state is
shown to change continuously from an elastic flow to a channel-like, plastic
flow as the disorder strength is increased.Comment: 31 pages, RevTex 3.0, 15 figures upon request, accepted for
publication in Phys. Rev. B., HAF94MD
A Simple Model for the DNA Denaturation Transition
We study pairs of interacting self-avoiding walks on the 3d simple cubic
lattice. They have a common origin and are allowed to overlap only at the same
monomer position along the chain. The latter overlaps are indeed favored by an
energetic gain.
This is inspired by a model introduced long ago by Poland and Sheraga [J.
Chem. Phys. {\bf 45}, 1464 (1966)] for the denaturation transition in DNA
where, however, self avoidance was not fully taken into account. For both
models, there exists a temperature T_m above which the entropic advantage to
open up overcomes the energy gained by forming tightly bound two-stranded
structures.
Numerical simulations of our model indicate that the transition is of first
order (the energy density is discontinuous), but the analog of the surface
tension vanishes and the scaling laws near the transition point are exactly
those of a second order transition with crossover exponent \phi=1. Numerical
and exact analytic results show that the transition is second order in modified
models where the self-avoidance is partially or completely neglected.Comment: 29 pages, LaTeX, 20 postscript figure
Universal finite-size scaling analysis of Ising models with long-range interactions at the upper critical dimensionality: Isotropic case
We investigate a two-dimensional Ising model with long-range interactions
that emerge from a generalization of the magnetic dipolar interaction in spin
systems with in-plane spin orientation. This interaction is, in general,
anisotropic whereby in the present work we focus on the isotropic case for
which the model is found to be at its upper critical dimensionality. To
investigate the critical behavior the temperature and field dependence of
several quantities are studied by means of Monte Carlo simulations. On the
basis of the Privman-Fisher hypothesis and results of the renormalization group
the numerical data are analyzed in the framework of a finite-size scaling
analysis and compared to finite-size scaling functions derived from a
Ginzburg-Landau-Wilson model in zero mode (mean-field) approximation. The
obtained excellent agreement suggests that at least in the present case the
concept of universal finite-size scaling functions can be extended to the upper
critical dimensionality.Comment: revtex4, 10 pages, 5 figures, 1 tabl
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