49 research outputs found
Continuous Elastic Phase Transitions in Pure and Disordered Crystals
We review the theory of second--order (ferro--)elastic phase transitions,
where the order parameter consists of a certain linear combination of strain
tensor components, and the accompanying soft mode is an acoustic phonon. In
three--dimensional crystals, the softening can occur in one-- or
two--dimensional soft sectors. The ensuing anisotropy reduces the effect of
fluctuations, rendering the critical behaviour of these systems classical for a
one--dimensional soft sector, and classical with logarithmic corrections in
case of a two--dimensional soft sector. The dynamical critical exponent is , and as a consequence the sound velocity vanishes as , while the phonon damping coefficient is essentially
temperature--independent. Disorder may lead to a variety of precursor effects
and modified critical behaviour. Defects that locally soften the crystal may
induce the phenomenon of local order parameter condensation. When the
correlation length of the pure system exceeds the average defect separation
, a disorder--induced phase transition to a state with
non--zero average order parameter can occur at a temperature
well above the transition temperature of the pure crystal. Near
, the order--parameter curve, susceptibility, and specific heat appear
rounded. For the spatial inhomogeneity induces a static
central peak with finite width in the scattering cross section, accompanied
by a dynamical component that is confined to the very vicinity of the
disorder--induced phase transition.Comment: 26 pages, Latex (rs.sty now IS included), 11 figures can be obtained
from U.C. T\"auber ([email protected]); will appear in Phil. Trans. Roy.
Soc. Lond. A (October 1996
Self-averaging in the random 2D Ising ferromagnet
We study sample-to-sample fluctuations in a critical two-dimensional Ising
model with quenched random ferromagnetic couplings. Using replica calculations
in the renormalization group framework we derive explicit expressions for the
probability distribution function of the critical internal energy and for the
specific heat fluctuations. It is shown that the disorder distribution of
internal energies is Gaussian, and the typical sample-to-sample fluctuations as
well as the average value scale with the system size like . In contrast, the specific heat is shown to be self-averaging with a
distribution function that tends to a -peak in the thermodynamic limit
. While previously a lack of self-averaging was found for the
free energy, we here obtain results for quantities that are directly measurable
in simulations, and implications for measurements in the actual lattice system
are discussed.Comment: 12 pages, accepted versio
Quantum Hall effect at low magnetic fields
The temperature and scale dependence of resistivities in the standard scaling
theory of the integer quantum Hall effect is discussed. It is shown that recent
experiments, claiming to observe a discrepancy with the global phase diagram of
the quantum Hall effect, are in fact in agreement with the standard theory. The
apparent low-field transition observed in the experiments is identified as a
crossover due to weak localization and a strong reduction of the conductivity
when Landau quantization becomes dominant.Comment: 4 pages, 2 figures, minor corrections, to appear in PR
Dynamical scaling at the quantum Hall transition: Coulomb blockade versus phase breaking
We argue that the finite temperature dynamics of the integer quantum Hall
system is governed by two independent length scales. The consistent scaling
description of the transition makes crucial use of two temperature critical
exponents, reflecting the interplay between charging effects and
interaction-induced dephasing. Experimental implications of the two-scale
picture are discussed.Comment: 4 pages, RevTeX, 1 figure included, minor changes, accepted in PR
Scaling in the Integer Quantum Hall Effect: interactions and low magnetic fields
Recent developments in the scaling theory of the integer quantum Hall effect
are discussed. In particular, the influence of electron-electron interactions
on the critical behavior are studied. It is further argued that recent
experiments on the disappearance of the quantum Hall effect at low magnetic
fields support rather than disprove the scaling theory, when interpreted
properly.Comment: 13 pages, invited talk at DPG spring meeting, Regensburg, March 2000,
to appear in Advances in Solid State Physics, ed. B. Krame
Disorder and Quantum Fluctuations in Superconducting Films in Strong Magnetic Fields
We find that the upper critical field in a two-dimensional disordered
superconductor can increase essentially at low temperatures. This happens due
to the formation of local superconducting islands weakly coupled via the
Josephson effect. The distribution of the superconducting islands is derived.
It is shown that the value of the critical field is determined by the interplay
of the proximity effect and quantum phase fluctuations. We find that the shift
of the upper critical field is connected with the pinning properties of a
superconductor.Comment: 4 page
Exact renormalization-group analysis of first order phase transitions in clock models
We analyze the exact behavior of the renormalization group flow in
one-dimensional clock-models which undergo first order phase transitions by the
presence of complex interactions. The flow, defined by decimation, is shown to
be single-valued and continuous throughout its domain of definition, which
contains the transition points. This fact is in disagreement with a recently
proposed scenario for first order phase transitions claiming the existence of
discontinuities of the renormalization group. The results are in partial
agreement with the standard scenario. However in the vicinity of some fixed
points of the critical surface the renormalized measure does not correspond to
a renormalized Hamiltonian for some choices of renormalization blocks. These
pathologies although similar to Griffiths-Pearce pathologies have a different
physical origin: the complex character of the interactions. We elucidate the
dynamical reason for such a pathological behavior: entire regions of coupling
constants blow up under the renormalization group transformation. The flows
provide non-perturbative patterns for the renormalization group behavior of
electric conductivities in the quantum Hall effect.Comment: 13 pages + 3 ps figures not included, TeX, DFTUZ 91.3
Effect of screening of the Coulomb interaction on the conductivity in the quantum Hall regime
We study variable range hopping in the quantum Hall effect regime in the
presence of a metallic gate parallel to the plane of a two-dimensional electron
gas. Screening of the Coulomb interaction by the gate causes the partial
``filling'' of the Coulomb gap in the density of localized states. At low
enough temperatures this leads to a substantial enhancement and a new
temperature behavior of the hopping conductivity. As a result, the diagonal
conductivity peaks become much wider. The power law dependence of the width of
the peaks on the temperature changes: the corresponding exponent turns out to
be twice as small as that for gateless structures. The width dependences on the
current in non-ohmic regime and on the frequency for the absorption of the
electromagnetic waves experience a similar modification. The experimental
observation of the crossovers predicted may demonstrate the important role of
the Coulomb interaction in the integer quantum Hall regime.Comment: 14 pages + 3 figures by request preprint TPI-MINN-93/58-
Information about the Integer Quantum Hall Transition Extracted from the Autocorrelation Function of Spectral Determinants
The Autocorrelation function of spectral determinants (ASD) is used to probe
the sensitivity of a two-dimensional disordered electron gas to the system's
size L.
For weak magnetic fields ASD is shown to depend only trivially on L, which is
a strong indication that all states are localized.
From nontrivial dependence of ASD on L for infinite L at a Hall conductance
of 1/2 e^2/h we deduce the existence of critical wave functions at this point,
as long as the disorder strength does not exceed a critical value.Comment: 4 pages, one citation correcte
Dualities in Quantum Hall System and Noncommutative Chern-Simons Theory
We discuss different dualities of QHE in the framework of the noncommutative
Chern-Simons theory. First, we consider the Morita or T-duality transformation
on the torus which maps the abelian noncommutative CS description of QHE on the
torus into the nonabelian commutative description on the dual torus. It is
argued that the Ruijsenaars integrable many-body system provides the
description of the QHE with finite amount of electrons on the torus. The new
IIB brane picture for the QHE is suggested and applied to Jain and generalized
hierarchies. This picture naturally links 2d -model and 3d CS
description of the QHE. All duality transformations are identified in the brane
setup and can be related with the mirror symmetry and S duality. We suggest a
brane interpretation of the plateu transition in IQHE in which a critical point
is naturally described by WZW model.Comment: 31 pages, 4 figure