208 research outputs found
Field-Theoretic Techniques in the Study of Critical Phenomena
We shortly illustrate how the field-theoretic approach to critical phenomena
takes place in the more complete Wilson theory of renormalization and
qualitatively discuss its domain of validity. By the way, we suggest that the
differential renormalization functions (like the beta-function) of the
perturbative scalar theory in four dimensions should be Borel summable provided
they are calculated within a minimal subtraction scheme.Comment: 32 pages, LaTeX, 9 figures, to appear in Journal of Physical Studie
Universality and quantum effects in one-component critical fluids
Non-universal scale transformations of the physical fields are extended to
pure quantum fluids and used to calculate susceptibility, specific heat and the
order parameter along the critical isochore of He3 near its liquid-vapor
critical point. Within the so-called preasymptotic domain, where the Wegner
expansion restricted to the first term of confluent corrections to scaling is
expected valid, the results show agreement with the experimental measurements
and recent predictions, either based on the minimal-substraction
renormalization and the massive renormalization schemes within the
-model, or based on the crossover parametric equation of
state for Ising-like systems
Nonasymptotic critical behavior from field theory
The obtention (up to five or six loop orders) of nonasymptotic critical
behavior, above and below Tc, from the field theoretical framework is presented
and discussed.Comment: 9 page
Renormalization group domains of the scalar Hamiltonian
Using the local potential approximation of the exact renormalization group
(RG) equation, we show the various domains of values of the parameters of the
O(1)-symmetric scalar Hamiltonian. In three dimensions, in addition to the
usual critical surface (attraction domain of the Wilson-Fisher fixed
point), we explicitly show the existence of a first-order phase transition
domain separated from by the tricritical surface
(attraction domain of the Gaussian fixed point). and are two
distinct domains of repulsion for the Gaussian fixed point, but is not
the basin of attraction of a fixed point. is characterized by an
endless renormalized trajectory lying entirely in the domain of negative values
of the -coupling. This renormalized trajectory exists also in four
dimensions making the Gaussian fixed point ultra-violet stable (and the
renormalized field theory asymptotically free but with a wrong
sign of the perfect action). We also show that very retarded classical-to-Ising
crossover may exist in three dimensions (in fact below four dimensions). This
could be an explanation of the unexpected classical critical behavior observed
in some ionic systems.Comment: 13 pages, 6 figures, to appear in Cond. Matt. Phys, some minor
correction
Large-N_f chiral transition in the Yukawa model
We investigate the finite-temperature behavior of the Yukawa model in which
fermions are coupled with a scalar field in the limit . Close to the chiral transition the model shows a crossover between
mean-field behavior (observed for ) and Ising behavior (observed
for any finite ). We show that this crossover is universal and related to
that observed in the weakly-coupled theory. It corresponds to the
renormalization-group flow from the unstable Gaussian fixed point to the stable
Ising fixed point. This equivalence allows us to use results obtained in field
theory and in medium-range spin models to compute Yukawa correlation functions
in the crossover regime
Classical-to-critical crossovers from field theory
We extent the previous determinations of nonasymptotic critical behavior of
Phys. Rev B32, 7209 (1985) and B35, 3585 (1987) to accurate expressions of the
complete classical-to-critical crossover (in the 3-d field theory) in terms of
the temperature-like scaling field (i.e., along the critical isochore) for : 1)
the correlation length, the susceptibility and the specific heat in the
homogeneous phase for the n-vector model (n=1 to 3) and 2) for the spontaneous
magnetization (coexistence curve), the susceptibility and the specific heat in
the inhomogeneous phase for the Ising model (n=1). The present calculations
include the seventh loop order of Murray and Nickel (1991) and closely account
for the up-to-date estimates of universal asymptotic critical quantities
(exponents and amplitude combinations) provided by Guida and Zinn-Justin [J.
Phys. A31, 8103 (1998)].Comment: 4 figs, 4 program documents in appendix, some corrections adde
Antisymmetric and other subleading corrections to scaling in the local potential approximation
For systems in the universality class of the three-dimensional Ising model we
compute the critical exponents in the local potential approximation (LPA), that
is, in the framework of the Wegner-Houghton equation. We are mostly interested
in antisymmetric corrections to scaling, which are relatively poorly studied.
We find the exponent for the leading antisymmetric correction to scaling
in the LPA. This high value implies that such
corrections cannot explain asymmetries observed in some Monte Carlo
simulations.Comment: 12 pages, 3 Postscript figures, uses eps
Field Theoretic Calculation of the Universal Amplitude Ratio of Correlation Lengths in 3D-Ising Systems
In three-dimensional systems of the Ising universality class the ratio of
correlation length amplitudes for the high- and low-temperature phases is a
universal quantity. Its field theoretic determination apart from the
-expansion represents a gap in the existing literature. In this
article we present a method, which allows to calculate this ratio by
renormalized perturbation theory in the phases with unbroken and broken
symmetry of a one-component -theory in fixed dimensions . The
results can be expressed as power series in the renormalized coupling constant
of either of the two phases, and with the knowledge of their fixed point values
numerical estimates are obtainable. These are given for the case of a two-loop
calculation.Comment: 14 pages, MS-TPI-94-0
Crossover scaling from classical to nonclassical critical behavior
We study the crossover between classical and nonclassical critical behaviors.
The critical crossover limit is driven by the Ginzburg number G. The
corresponding scaling functions are universal with respect to any possible
microscopic mechanism which can vary G, such as changing the range or the
strength of the interactions. The critical crossover describes the unique flow
from the unstable Gaussian to the stable nonclassical fixed point. The scaling
functions are related to the continuum renormalization-group functions. We show
these features explicitly in the large-N limit of the O(N) phi^4 model. We also
show that the effective susceptibility exponent is nonmonotonic in the
low-temperature phase of the three-dimensional Ising model.Comment: 5 pages, final version to appear in Phys. Rev.
Universal sextic effective interaction at criticality
The renormalization group approach in three dimensions is used to estimate
the universal critical value g_6^* of the dimensionless sextic effective
coupling constant for the Ising model. The four-loop RG expansion for g_6 is
calculated and resummed by means of the Pade-Borel and Pade-Borel-Leroy
procedures resulting in g_6^* = 1.596, while the most accurate estimate for
g_6^* is argued to be equal to 1.61.Comment: 6 pages, TeX, no figure
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