1,240 research outputs found
Order Parameter Description of the Anderson-Mott Transition
An order parameter description of the Anderson-Mott transition (AMT) is
given. We first derive an order parameter field theory for the AMT, and then
present a mean-field solution. It is shown that the mean-field critical
exponents are exact above the upper critical dimension. Renormalization group
methods are then used to show that a random-field like term is generated under
renormalization. This leads to similarities between the AMT and random-field
magnets, and to an upper critical dimension for the AMT. For
, an expansion is used to calculate the critical
exponents. To first order in they are found to coincide with the
exponents for the random-field Ising model. We then discuss a general scaling
theory for the AMT. Some well established scaling relations, such as Wegner's
scaling law, are found to be modified due to random-field effects. New
experiments are proposed to test for random-field aspects of the AMT.Comment: 28pp., REVTeX, no figure
Local versus Nonlocal Order Parameter Field Theories for Quantum Phase Transitions
General conditions are formulated that allow to determine which quantum phase
transitions in itinerant electron systems can be described by a local
Landau-Ginzburg-Wilson or LGW theory solely in terms of the order parameter. A
crucial question is the degree to which the order parameter fluctuations couple
to other soft modes. Three general classes of zero-wavenumber order parameters,
in the particle-hole spin-singlet and spin-triplet channels, and in the
particle-particle channel, respectively, are considered. It is shown that the
particle-hole spin-singlet class does allow for a local LGW theory, while the
other two classes do not. The implications of this result for the critical
behavior at various quantum phase transitions are discussed, as is the
connection with nonanalyticities in the wavenumber dependence of order
parameter susceptibilities in the disordered phase.Comment: 9 pp., LaTeX, no figs, final version as publishe
Split transition in ferromagnetic superconductors
The split superconducting transition of up-spin and down-spin electrons on
the background of ferromagnetism is studied within the framework of a recent
model that describes the coexistence of ferromagnetism and superconductivity
induced by magnetic fluctuations. It is shown that one generically expects the
two transitions to be close to one another. This conclusion is discussed in
relation to experimental results on URhGe. It is also shown that the magnetic
Goldstone modes acquire an interesting structure in the superconducting phase,
which can be used as an experimental tool to probe the origin of the
superconductivity.Comment: REVTeX4, 15 pp, 7 eps fig
On the critical behavior of disordered quantum magnets: The relevance of rare regions
The effects of quenched disorder on the critical properties of itinerant
quantum antiferromagnets and ferromagnets are considered. Particular attention
is paid to locally ordered spatial regions that are formed in the presence of
quenched disorder even when the bulk system is still in the paramagnetic phase.
These rare regions or local moments are reflected in the existence of spatially
inhomogeneous saddle points of the Landau-Ginzburg-Wilson functional. We derive
an effective theory that takes into account small fluctuations around all of
these saddle points. The resulting free energy functional contains a new term
in addition to those obtained within the conventional perturbative approach,
and it comprises what would be considered non-perturbative effects within the
latter. A renormalization group analysis shows that in the case of
antiferromagnets, the previously found critical fixed point is unstable with
respect to this new term, and that no stable critical fixed point exists at
one-loop order. This is contrasted with the case of itinerant ferromagnets,
where we find that the previously found critical behavior is unaffected by the
rare regions due to an effective long-ranged interaction between the order
parameter fluctuations.Comment: 16 pp., REVTeX, epsf, 2 figs, final version as publishe
The Anderson-Mott Transition as a Random-Field Problem
The Anderson-Mott transition of disordered interacting electrons is shown to
share many physical and technical features with classical random-field systems.
A renormalization group study of an order parameter field theory for the
Anderson-Mott transition shows that random-field terms appear at one-loop
order. They lead to an upper critical dimension for this model.
For the critical behavior is mean-field like. For an
-expansion yields exponents that coincide with those for the
random-field Ising model. Implications of these results are discussed.Comment: 8pp, REVTeX, db/94/
The effect of rare regions on a disordered itinerant quantum antiferromagnet with cubic anisotropy
We study the quantum phase transition of an itinerant antiferromagnet with
cubic anisotropy in the presence of quenched disorder, paying particular
attention to the locally ordered spatial regions that form in the Griffiths
region. We derive an effective action where these rare regions are described in
terms of static annealed disorder. A one loop renormalization group analysis of
the effective action shows that for order parameter dimensions the rare
regions destroy the conventional critical behavior. For order parameter
dimensions the critical behavior is not influenced by the rare regions,
it is described by the conventional dirty cubic fixed point. We also discuss
the influence of the rare regions on the fluctuation-driven first-order
transition in this system.Comment: 6 pages RevTe
Exact multilocal renormalization on the effective action : application to the random sine Gordon model statics and non-equilibrium dynamics
We extend the exact multilocal renormalization group (RG) method to study the
flow of the effective action functional. This important physical quantity
satisfies an exact RG equation which is then expanded in multilocal components.
Integrating the nonlocal parts yields a closed exact RG equation for the local
part, to a given order in the local part. The method is illustrated on the O(N)
model by straightforwardly recovering the exponent and scaling
functions. Then it is applied to study the glass phase of the Cardy-Ostlund,
random phase sine Gordon model near the glass transition temperature. The
static correlations and equilibrium dynamical exponent are recovered and
several new results are obtained. The equilibrium two-point scaling functions
are obtained. The nonequilibrium, finite momentum, two-time response and
correlations are computed. They are shown to exhibit scaling forms,
characterized by novel exponents , as well as
universal scaling functions that we compute. The fluctuation dissipation ratio
is found to be non trivial and of the form . Analogies and
differences with pure critical models are discussed.Comment: 33 pages, RevTe
Superconducting ``metals'' and ``insulators''
We propose a characterization of zero temperature phases in disordered
superconductors on the basis of the nature of quasiparticle transport. In three
dimensional systems, there are two distinct phases in close analogy to the
distinction between normal metals and insulators: the superconducting "metal"
with delocalized quasiparticle excitations and the superconducting "insulator"
with localized quasiparticles. We describe experimental realizations of either
phase, and study their general properties theoretically. We suggest experiments
where it should be possible to tune from one superconducting phase to the
other, thereby probing a novel "metal-insulator" transition inside a
superconductor. We point out various implications of our results for the phase
transitions where the superconductor is destroyed at zero temperature to form
either a normal metal or a normal insulator.Comment: 18 page
Properties of the random field Ising model in a transverse magnetic field
We consider the effect of a random longitudinal field on the Ising model in a
transverse magnetic field. For spatial dimension , there is at low
strength of randomness and transverse field, a phase with true long range order
which is destroyed at higher values of the randomness or transverse field. The
properties of the quantum phase transition at zero temperature are controlled
by a fixed point with no quantum fluctuations. This fixed point also controls
the classical finite temperature phase transition in this model. Many critical
properties of the quantum transition are therefore identical to those of the
classical transition. In particular, we argue that the dynamical scaling is
activated, i.e, the logarithm of the diverging time scale rises as a power of
the diverging length scale
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