54 research outputs found
A new class of short distance universal amplitude ratios
We propose a new class of universal amplitude ratios which involve the first
terms of the short distance expansion of the correlators of a statistical model
in the vicinity of a critical point. We will describe the critical system with
a conformal field theory (UV fixed point) perturbed by an appropriate relevant
operator. In two dimensions the exact knowledge of the UV fixed point allows
for accurate predictions of the ratios and in many nontrivial integrable
perturbations they can even be evaluated exactly. In three dimensional O(N)
scalar systems feasible extensions of some existing results should allow to
obtain perturbative expansions for the ratios. By construction these universal
ratios are a perfect tool to explore the short distance properties of the
underlying quantum field theory even in regimes where the correlation length
and one point functions are not accessible in experiments or simulations.Comment: 8 pages, revised version, references adde
Critical adsorption on curved objects
A systematic fieldtheoretic description of critical adsorption on curved
objects such as spherical or rodlike colloidal particles immersed in a fluid
near criticality is presented. The temperature dependence of the corresponding
order parameter profiles and of the excess adsorption are calculated
explicitly. Critical adsorption on elongated rods is substantially more
pronounced than on spherical particles. It turns out that, within the context
of critical phenomena in confined geometries, critical adsorption on a
microscopically thin `needle' represents a distinct universality class of its
own. Under favorable conditions the results are relevant for the flocculation
of colloidal particles.Comment: 52 pages, 10 figure
Integrable field theory and critical phenomena. The Ising model in a magnetic field
The two-dimensional Ising model is the simplest model of statistical
mechanics exhibiting a second order phase transition. While in absence of
magnetic field it is known to be solvable on the lattice since Onsager's work
of the forties, exact results for the magnetic case have been missing until the
late eighties, when A.Zamolodchikov solved the model in a field at the critical
temperature, directly in the scaling limit, within the framework of integrable
quantum field theory. In this article we review this field theoretical approach
to the Ising universality class, with particular attention to the results
obtained starting from Zamolodchikov's scattering solution and to their
comparison with the numerical estimates on the lattice. The topics discussed
include scattering theory, form factors, correlation functions, universal
amplitude ratios and perturbations around integrable directions. Although we
restrict our discussion to the Ising model, the emphasis is on the general
methods of integrable quantum field theory which can be used in the study of
all universality classes of critical behaviour in two dimensions.Comment: 42 pages; invited review article for J. Phys.
Specific heat amplitude ratios for anisotropic Lifshitz critical behaviors
We determine the specific heat amplitude ratio near a -axial Lifshitz
point and show its universal character. Using a recent renormalization group
picture along with new field-theoretical -expansion techniques,
we established this amplitude ratio at one-loop order. We estimate the
numerical value of this amplitude ratio for and . The result is in
very good agreement with its experimental measurement on the magnetic material
. It is shown that in the limit it trivially reduces to the
Ising-like amplitude ratio.Comment: 8 pages, RevTex, accepted as a Brief Report in Physical Review
Density Fluctuations in an Electrolyte from Generalized Debye-Hueckel Theory
Near-critical thermodynamics in the hard-sphere (1,1) electrolyte is well
described, at a classical level, by Debye-Hueckel (DH) theory with (+,-) ion
pairing and dipolar-pair-ionic-fluid coupling. But DH-based theories do not
address density fluctuations. Here density correlations are obtained by
functional differentiation of DH theory generalized to {\it non}-uniform
densities of various species. The correlation length diverges universally
at low density as (correcting GMSA theory). When
one has as
where the amplitudes compare informatively with experimental data.Comment: 5 pages, REVTeX, 1 ps figure included with epsf. Minor changes,
references added. Accepted for publication in Phys. Rev. Let
Updated tests of scaling and universality for the spin-spin correlations in the 2D and 3D spin-S Ising models using high-temperature expansions
We have extended, from order 12 through order 25, the high-temperature series
expansions (in zero magnetic field) for the spin-spin correlations of the
spin-S Ising models on the square, simple-cubic and body-centered-cubic
lattices. On the basis of this large set of data, we confirm accurately the
validity of the scaling and universality hypotheses by resuming several tests
which involve the correlation function, its moments and the exponential or the
second-moment correlation-lengths.Comment: 21 pages, 8 figure
Equilibrium random-field Ising critical scattering in the antiferromagnet Fe(0.93)Zn(0.07)F2
It has long been believed that equilibrium random-field Ising model (RFIM)
critical scattering studies are not feasible in dilute antiferromagnets close
to and below Tc(H) because of severe non-equilibrium effects. The high magnetic
concentration Ising antiferromagnet Fe(0.93)Zn(0.07)F2, however, does provide
equilibrium behavior. We have employed scaling techniques to extract the
universal equilibrium scattering line shape, critical exponents nu = 0.87 +-
0.07 and eta = 0.20 +- 0.05, and amplitude ratios of this RFIM system.Comment: 4 pages, 1 figure, minor revision
Dynamic structure factor of the Ising model with purely relaxational dynamics
We compute the dynamic structure factor for the Ising model with a purely
relaxational dynamics (model A). We perform a perturbative calculation in the
expansion, at two loops in the high-temperature phase and at one
loop in the temperature magnetic-field plane, and a Monte Carlo simulation in
the high-temperature phase. We find that the dynamic structure factor is very
well approximated by its mean-field Gaussian form up to moderately large values
of the frequency and momentum . In the region we can investigate,
, , where is the correlation
length and the zero-momentum autocorrelation time, deviations are at
most of a few percent.Comment: 21 pages, 3 figure
Critical behavior of the three-dimensional XY universality class
We improve the theoretical estimates of the critical exponents for the
three-dimensional XY universality class. We find alpha=-0.0146(8),
gamma=1.3177(5), nu=0.67155(27), eta=0.0380(4), beta=0.3485(2), and
delta=4.780(2). We observe a discrepancy with the most recent experimental
estimate of alpha; this discrepancy calls for further theoretical and
experimental investigations. Our results are obtained by combining Monte Carlo
simulations based on finite-size scaling methods, and high-temperature
expansions. Two improved models (with suppressed leading scaling corrections)
are selected by Monte Carlo computation. The critical exponents are computed
from high-temperature expansions specialized to these improved models. By the
same technique we determine the coefficients of the small-magnetization
expansion of the equation of state. This expansion is extended analytically by
means of approximate parametric representations, obtaining the equation of
state in the whole critical region. We also determine the specific-heat
amplitude ratio.Comment: 61 pages, 3 figures, RevTe
Bulk and Boundary Critical Behavior at Lifshitz Points
Lifshitz points are multicritical points at which a disordered phase, a
homogeneous ordered phase, and a modulated ordered phase meet. Their bulk
universality classes are described by natural generalizations of the standard
model. Analyzing these models systematically via modern
field-theoretic renormalization group methods has been a long-standing
challenge ever since their introduction in the middle of the 1970s. We survey
the recent progress made in this direction, discussing results obtained via
dimensionality expansions, how they compare with Monte Carlo results, and open
problems. These advances opened the way towards systematic studies of boundary
critical behavior at -axial Lifshitz points. The possible boundary critical
behavior depends on whether the surface plane is perpendicular to one of the
modulation axes or parallel to all of them. We show that the semi-infinite
field theories representing the corresponding surface universality classes in
these two cases of perpendicular and parallel surface orientation differ
crucially in their Hamiltonian's boundary terms and the implied boundary
conditions, and explain recent results along with our current understanding of
this matter.Comment: Invited contribution to STATPHYS 22, to be published in the
Proceedings of the 22nd International Conference on Statistical Physics
(STATPHYS 22) of the International Union of Pure and Applied Physics (IUPAP),
4--9 July 2004, Bangalore, Indi
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