337 research outputs found
Is the droplet theory for the Ising spin glass inconsistent with replica field theory?
Symmetry arguments are used to derive a set of exact identities between
irreducible vertex functions for the replica symmetric field theory of the
Ising spin glass in zero magnetic field. Their range of applicability spans
from mean field to short ranged systems in physical dimensions. The replica
symmetric theory is unstable for d>8, just like in mean field theory. For 6<d<8
and d<6 the resummation of an infinite number of terms is necessary to settle
the problem. When d<8, these Ward-like identities must be used to distinguish
an Almeida-Thouless line from the replica symmetric droplet phase.Comment: 4 pages. Accepted for publication in J.Phys.A. This is the accepted
version with the following minor changes: one extra sentence in the abstract;
footnote 2 slightly extended; last paragraph somewhat reformulate
Finite dimensional corrections to mean field in a short-range p-spin glassy model
In this work we discuss a short range version of the -spin model. The
model is provided with a parameter that allows to control the crossover with
the mean field behaviour. We detect a discrepancy between the perturbative
approach and numerical simulation. We attribute it to non-perturbative effects
due to the finite probability that each particular realization of the disorder
allows for the formation of regions where the system is less frustrated and
locally freezes at a higher temperature.Comment: 18 pages, 5 figures, submitted to Phys Rev
Statistical mechanics of the random K-SAT model
The Random K-Satisfiability Problem, consisting in verifying the existence of
an assignment of N Boolean variables that satisfy a set of M=alpha N random
logical clauses containing K variables each, is studied using the replica
symmetric framework of diluted disordered systems. We present an exact
iterative scheme for the replica symmetric functional order parameter together
for the different cases of interest K=2, K>= 3 and K>>1. The calculation of the
number of solutions, which allowed us [Phys. Rev. Lett. 76, 3881 (1996)] to
predict a first order jump at the threshold where the Boolean expressions
become unsatisfiable with probability one, is thoroughly displayed. In the case
K=2, the (rigorously known) critical value (alpha=1) of the number of clauses
per Boolean variable is recovered while for K>=3 we show that the system
exhibits a replica symmetry breaking transition. The annealed approximation is
proven to be exact for large K.Comment: 34 pages + 1 table + 8 fig., submitted to Phys. Rev. E, new section
added and references update
Stability of self-consistent solutions for the Hubbard model at intermediate and strong coupling
We present a general framework how to investigate stability of solutions
within a single self-consistent renormalization scheme being a parquet-type
extension of the Baym-Kadanoff construction of conserving approximations. To
obtain a consistent description of one- and two-particle quantities, needed for
the stability analysis, we impose equations of motion on the one- as well on
the two-particle Green functions simultaneously and introduce approximations in
their input, the completely irreducible two-particle vertex. Thereby we do not
loose singularities caused by multiple two-particle scatterings. We find a
complete set of stability criteria and show that each instability, singularity
in a two-particle function, is connected with a symmetry-breaking order
parameter, either of density type or anomalous. We explicitly study the Hubbard
model at intermediate coupling and demonstrate that approximations with static
vertices get unstable before a long-range order or a metal-insulator transition
can be reached. We use the parquet approximation and turn it to a workable
scheme with dynamical vertex corrections. We derive a qualitatively new theory
with two-particle self-consistence, the complexity of which is comparable with
FLEX-type approximations. We show that it is the simplest consistent and stable
theory being able to describe qualitatively correctly quantum critical points
and the transition from weak to strong coupling in correlated electron systems.Comment: REVTeX, 26 pages, 12 PS figure
Parquet approach to nonlocal vertex functions and electrical conductivity of disordered electrons
A diagrammatic technique for two-particle vertex functions is used to
describe systematically the influence of spatial quantum coherence and
backscattering effects on transport properties of noninteracting electrons in a
random potential. In analogy with many-body theory we construct parquet
equations for topologically distinct {\em nonlocal} irreducible vertex
functions into which the {\em local} one-particle propagator and two-particle
vertex of the coherent-potential approximation (CPA) enter as input. To
complete the two-particle parquet equations we use an integral form of the Ward
identity and determine the one-particle self-energy from the known irreducible
vertex. In this way a conserving approximation with (Herglotz) analytic
averaged Green functions is obtained. We use the limit of high spatial
dimensions to demonstrate how nonlocal corrections to the (CPA)
solution emerge. The general parquet construction is applied to the calculation
of vertex corrections to the electrical conductivity. With the aid of the
high-dimensional asymptotics of the nonlocal irreducible vertex in the
electron-hole scattering channel we derive a mean-field approximation for the
conductivity with vertex corrections. The impact of vertex corrections onto the
electronic transport is assessed quantitatively within the proposed mean-field
description on a binary alloy.Comment: REVTeX 19 pages, 9 EPS diagrams, 6 PS figure
Large negative velocity gradients in Burgers turbulence
We consider 1D Burgers equation driven by large-scale white-in-time random
force. The tails of the velocity gradients probability distribution function
(PDF) are analyzed by saddle-point approximation in the path integral
describing the velocity statistics. The structure of the saddle-point
(instanton), that is velocity field configuration realizing the maximum of
probability, is studied numerically in details. The numerical results allow us
to find analytical solution for the long-time part of the instanton. Its
careful analysis confirms the result of [Phys. Rev. Lett. 78 (8) 1452 (1997)
[chao-dyn/9609005]] based on short-time estimations that the left tail of PDF
has the form ln P(u_x) \propto -|u_x|^(3/2).Comment: 10 pages, RevTeX, 10 figure
Static chaos and scaling behaviour in the spin-glass phase
We discuss the problem of static chaos in spin glasses. In the case of
magnetic field perturbations, we propose a scaling theory for the spin-glass
phase. Using the mean-field approach we argue that some pure states are
suppressed by the magnetic field and their free energy cost is determined by
the finite-temperature fixed point exponents. In this framework, numerical
results suggest that mean-field chaos exponents are probably exact in finite
dimensions. If we use the droplet approach, numerical results suggest that the
zero-temperature fixed point exponent is very close to
. In both approaches is the lower critical dimension in
agreement with recent numerical simulations.Comment: 28 pages + 6 figures, LateX, figures uuencoded at the end of fil
Viscous Instanton for Burgers' Turbulence
We consider the tails of probability density functions (PDF) for different
characteristics of velocity that satisfies Burgers equation driven by a
large-scale force. The saddle-point approximation is employed in the path
integral so that the calculation of the PDF tails boils down to finding the
special field-force configuration (instanton) that realizes the extremum of
probability. We calculate high moments of the velocity gradient
and find out that they correspond to the PDF with where is the
Reynolds number. That stretched exponential form is valid for negative
with the modulus much larger than its root-mean-square (rms)
value. The respective tail of PDF for negative velocity differences is
steeper than Gaussian, , as well as
single-point velocity PDF . For high
velocity derivatives , the general formula is found:
.Comment: 15 pages, RevTeX 3.
Replica field theory and renormalization group for the Ising spin glass in an external magnetic field
We use the generic replica symmetric cubic field-theory to study the
transition of short range Ising spin glasses in a magnetic field around the
upper critical dimension, d=6. A novel fixed-point is found, in addition to the
well-known zero magnetic field fixed-point, from the application of the
renormalization group. In the spin glass limit, n going to 0, this fixed-point
governs the critical behaviour of a class of systems characterised by a single
cubic interaction parameter. For this universality class, the spin glass
susceptibility diverges at criticality, whereas the longitudinal mode remains
massive. The third mode, the so-called anomalous one, however, behaves
unusually, having a jump at criticality. The physical consequences of this
unusual behaviour are discussed, and a comparison with the conventional de
Almeida-Thouless scenario presented.Comment: 5 pages written in revtex4. Accepted for publication in Phys. Rev.
Let
HTL Resummation of the Thermodynamic Potential
Starting from the Phi-derivable approximation scheme at leading-loop order,
the thermodynamical potential in a hot scalar theory, as well as in QED and
QCD, is expressed in terms of hard thermal loop propagators. This
nonperturbative approach is consistent with the leading-order perturbative
results, ultraviolet finite, and, for gauge theories, explicitly
gauge-invariant. For hot QCD it is argued that the resummed approximation is
applicable in the large-coupling regime, down to almost twice the transition
temperature.Comment: minor changes, to appear in PRD, 27 pages, 15 eps figure
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